In this section we will be graphing parabolas. Plug these values into both equations. Solving an Absolute Value Equation. For absolute value equations multiplied by a constant (for example, y = a | x |),if 0 < a < 1, then the graph is compressed, and if a > 1, it is stretched. The graph of the solution divides the number line into three sections. Copyright 2021 Leaf Group Ltd. / Leaf Group Media, All Rights Reserved. We also notice that the graph appears vertically stretched, because the width of the final graph on a horizontal line is not equal to 2 times the vertical distance from the corner to this line, as it would be for an unstretched absolute value function. To solve an absolute value equation as $$\left | x+7 \right |=14$$ Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets. Inside the pages of this comprehensive workbook, students can learn algebra operations in a structured manner with a complete study program to help them understand essential math skills. Absolute Value in Algebra Absolute Value means ..... how far a number is from zero: "6" is 6 away from zero, and "â6" is also 6 away from zero. Found inside – Page 39Graphing. an. Absolute. Value. Equation. Absolute value equations can be graphed in a way that is similar to graphing linear equations. From this form, we can draw graphs. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade. Found inside – Page 317... 227 vertical, 228 entry, matrix, 256 equality graphing, 12–13 properties of, 8 solving, 10–12 equations. See also systems of equations absolute value, ... Set up two separate (and unrelated) equations for x in terms of y, being careful not to treat them as two equations in two variables: Because the original equation contained an absolute value, you're left with two relationships between x and y that are equally true. By continuing to browse this site, you are agreeing to our use of cookies. So when we're dealing with a variable, we need to consider both cases. Find out more here. Found insideSo for all values of greater than or equal to 1, the equation is just . ... We can graph absolute value functions by breaking them down algebraically as we ... Equation 2 is the correct one. Absolute value refers to a pointâs distance from zero or origin on the number line, regardless of the direction. The graph may or may not intersect the horizontal axis, depending on how the graph has been shifted and reflected. Now that we can graph an absolute value function, we will learn how to solve an absolute value equation. To solve this, you have to set up two equalities and solve each separately. Found inside – Page 1634 3 5 3 11 8 8 When absolute value is involved in algebraic equations, ... Technology Tip Use a graphing utility to display graphs ofy1 |x 3| and y2 8. You can also create an absolute value inequality simply by changing the equals sign to an inequality sign. The most significant feature of the absolute value graph is the corner point at which the graph changes direction. Found inside – Page iHave no fear! This un-intimidating guide walks you through all the essential topics, from absolute value and quadratic equations to logarithms and exponential functions to trig identities and matrix operations. An absolute value equation will always form a âVâ shape on your graph. The graph may or may not intersect the horizontal axis, depending on how the graph has been shifted and reflected. Set up two equations and solve them separately. DadsWorksheets.com Slope Calculator Found inside – Page 3GRAPHING ABSOLUTE VALUE EQUATIONS AND INEQUALITIES Absolute value equations have two possible solutions . There must be two different setups for each ... Absolute Value Equations Worksheet 1 - Here is a 16 problem multiple choice worksheet where you will determine the solutions to equations containing absolute value. Absolute value equations have two solutions. The easy way to score your highest on the SAT Whether you are a student struggling with math, reading, or writing essays, this updated edition of SAT For Dummies offers advice for tackling the toughest questions, as well as hints and tips ... Absolute Value Equations Worksheet 1 - Here is a 16 problem multiple choice worksheet where you will determine the solutions to equations containing absolute value. Example 1 Absolute minimum and maximum at stationary points Absolute minimum and maximum of a function may happen at local minimum and maximum respectively as shown in the graph below. These elements all reflect the author's philosophy of teaching, and the concepts are continually reinforced throughout the text by the thoughtful and well-designed use of pedagogy. General Formula for Absolute Value Inequality Graph and Solution. Type in any equation to get the solution, steps and graph This website uses cookies to ensure you get the best experience. This article reviews how to draw the graphs of absolute value functions. Found insideIts use is allowed on the major college entrance exams. This book is a nuts-and-bolts guide to working with the TI-Nspire, providing everything you need to get up and running and helping you get the most out of this high-powered math tool. \\ 2: \quad 4 = \frac{2}{5}×10 = 20/5 = 4 \rarr \text{ True!}. An absolute value equation is an equation that contains an absolute value expression. SOS Math: Solving Equations Containing Absolute Values, Purple Math: Solving Simpler Absolute-Value Equations. From this form, we can draw graphs. To solve an absolute value equation, we first isolate the absolute value expression using the same procedures we used to solve linear equations. The argument of this absolute value will be negative before the breakpoint (at x = 3) and positive after. More generally, the form of the equation for an absolute value function is y = a | x â h | + k. Also: This easy-to-use packet is chock full of stimulating activities that will jumpstart your students' interest in algebra while reinforcing major concepts. Scaling & reflecting absolute value functions: equation, Scaling & reflecting absolute value functions: graph, Practice: Scale & reflect absolute value graphs. The Student Solutions Manual provides worked solutions to the odd-numbered problems. In the picture below, you can see generalized example of absolute value equation and also the topic of this web page: absolute value inequalities . Absolute Value Symbol. Multiply each value of x by 2/3 (for example, if x= 2 then y will be 2/3 times 2 or 4/3). [latex]\begin{cases}f\left(x\right)=2\left|x - 3\right|-2,\hfill & \text{treating the stretch as a vertical stretch, or}\hfill \\ f\left(x\right)=\left|2\left(x - 3\right)\right|-2,\hfill & \text{treating the stretch as a horizontal compression}.\hfill \end{cases}[/latex], [latex]f\left(x\right)=a|x - 3|-2[/latex], [latex]\begin{cases}2=a|1 - 3|-2\hfill \\ 4=2a\hfill \\ a=2\hfill \end{cases}[/latex], http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175. Perplexed by polynomials? Don’t worry! This friendly guide takes the torture out of trigonometry by explaining everything in plain English, offering lots of easy-to-grasp examples, and adding a dash of humor and fun. It is possible for the absolute value function to intersect the horizontal axis at zero, one, or two points. The graph of an absolute value function will intersect the vertical axis when the input is zero. Consider absolute value as the distance from one point to another point. The absolute value is isolated on the left-hand side of the equation, so it's already set up for me to split the equation into two cases. Intermediate Algebra covers: Real Number Operations; Exponents ; Radicals; Fractional Exponents; Factoring Polynomials; Solving quadratic equations and applications; Graphs, Slopes, Intercepts, and Equations of Straight Lines; Graphs of ... Add arrows to the ends to show that the line extends further than the ⦠The absolute value of a number is always positive. If you're seeing this message, it means we're having trouble loading external resources on our website. With guidance and practice problems that reflect the most recent information, this edition takes the best-selling SAT guide and makes it even more relevant and useful. Found inside – Page 136Solving Absolute Value Equations and Inequalities Graphically Graphing is a powerful and important method for solving equations and inequalities . Found inside – Page 21When you are graphing a two-variable absolute value equation like y = |x|, remember that y cannot be negative. The graph will never go below the x-axis. Equation Inequality. Our printable absolute value worksheets meticulously designed for 6th grade and 7th grade students include exercises like finding the absolute value of positive and negative integers, performing simple addition, subtraction, multiplication and division involving the absolute value of real numbers and more. Find out more here. Regardless of direction, positive or negative, the distance between the two points is represented as a positive number or zero. If we couldn’t observe the stretch of the function from the graphs, could we algebraically determine it? Found inside – Page 721Solving Absolute Value Equations ○ Isolate the expression containing the absolute ... numerically using a table of values, or graphically using the graphs. If you already know the solution, you can tell immediately whether the number inside the absolute value brackets is positive or negative, and you can drop the absolute value brackets. In Other Type of Equations, we touched on the concepts of absolute value equations. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade. The book's organization makes it easy to adapt to a variety of course syllabi. The text expands on the fundamental concepts of algebra while addressing the needs of students with diverse backgrounds and learning styles. This point is shown at the origin. You can now drop the absolute value brackets from the original equation and write instead: Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. Suppose you know the point x = 4, y = 10 is on the line. His writing covers science, math and home improvement and design, as well as religion and the oriental healing arts. We also illustrate how to use completing the square to put the parabola into the form f(x)=a(x-h)^2+k. Our printable absolute value worksheets meticulously designed for 6th grade and 7th grade students include exercises like finding the absolute value of positive and negative integers, performing simple addition, subtraction, multiplication and division involving the absolute value of real numbers and more. Here is a set of practice problems to accompany the Absolute Value Inequalities section of the Solving Equations and Inequalities chapter of the notes for Paul Dawkins Algebra course at Lamar University. Add arrows to the ends to show that the line extends further than the edge of your graph⦠Found inside – Page 119Step 8 Model how to solve an absolute value inequality with less than. ... Refer to Step 7 for how to enter the equation, graph it, and determine the ... Found inside – Page 261Absolute Value Functions After reading the text, working the practice problems, ... Use a table of ordered pairs to graph an absolute value function. 2. Locate your first x value on the horizontal axis and go up to the y value you calculated and make a small dot. DadsWorksheets.com Slope Calculator The graph of [latex]y=|x|[/latex] has been shifted right 3 units, vertically stretched by a factor of 2, and shifted up 4 units. The absolute value of a complex number is defined by the Euclidean distance of its corresponding point in the complex ⦠Traces the development of mathematics from its beginnings in Babylonia and ancient Egypt to the work of Riemann and Godel in modern times Now available in a new three-volume paperback edition, Morris Kline's monumental work presents the ... By continuing to browse this site, you are agreeing to our use of cookies. This means that the corner point is located at [latex]\left(3,4\right)[/latex] for this transformed function. Found inside – Page 63Figure 4-6: The graph of the radical equation is symmetric. ... Figure 4-7 shows the graph of this absolute value equation. (10, 0) (–4, –2) Figure 4-7: The ... Absolute value equations are equations where the variable is within an absolute value operator, like |x-5|=9. Free absolute value equation calculator - solve absolute value equations with all the steps. Examples on absolute maximum and minimum of functions in different situations are discussed graphically. [Color Cover; Black-and-White Interior] Who says that learning math has to be boring?Your kids will love solving these fun emoji math puzzles, which cover topics including:-logical thinking -order of operations -fractions and ratios ... The basic absolute value function changes direction at the origin, so this graph has been shifted to the right 3 units and down 2 units from the basic toolkit function. If the number is negative, then the absolute value is its opposite: |-9|=9. To show we want the absolute value we put "|" marks either side (called "bars"), like these examples: Found inside – Page 130THE ABSOLUTE-VALUE FUNCTION To graph y = x , open the Y = editor and press Right cursor key 768 MATH ENTER ,TX , θ , n ) . Figure 6.1 shows the graph in a ... Also, if a is negative, then the graph opens downward, instead of upwards as usual. Since the complex numbers are not ordered, the definition given at the top for the real absolute value cannot be directly applied to complex numbers.However, the geometric interpretation of the absolute value of a real number as its distance from 0 can be generalised. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Need help with equations and inequalities of lines, two-variable linear absolute value, parabolas, and cubics? By using simple geometric shapes, this studyguide will help. 48 pages, 49 solved problems, all well-illustrated solutions. Found insideThis book will help you unlock all the magic, so you'll be able to use your TI-84 Plus for much more than basic math. The geometric mean is an average that is useful for sets of positive numbers, that are interpreted according to their product (as is the case with rates of growth) and not their sum (as is the case with the arithmetic mean): ¯ = (=) = For example, the geometric mean of five values: 4, 36, 45, 50, 75 is: = =Harmonic mean (HM) The harmonic mean is an average which is useful for sets of ⦠For absolute value equations multiplied by a constant (for example, y = a | x |),if 0 < a < 1, then the graph is compressed, and if a > 1, it is stretched. Our mission is to provide a free, world-class education to anyone, anywhere. We introduce the vertex and axis of symmetry for a parabola and give a process for graphing parabolas. Virginia Department of Education 2018 Grade 7 ⦠Absolute value means "distance from zero" on a number line. The general form of an absolute value function is f(x)=a|x-h|+k. Solve the equation for y; y will equal 2/3 x. Study Guide for College Algebra is a supplemental material for the basic text, College Algebra. (a) The absolute value function does not intersect the horizontal axis. Yes, they always intersect the vertical axis. Found inside – Page 2Know the definition of absolute value; simplify absolute value expressions. ... Know what it means to graph an equation and to write the equation of a graph ... No, they do not always intersect the horizontal axis. For a random number x, both the following equations are true: |-x| = x and |x| = x. Figure 8. Resource added for the Mathematics 108041 courses. Absolute Value Equation Worksheets. SAT MATH TEST BOOK The challenge is that the absolute value of a number depends on the number's sign: if it's positive, it's equal to the number: |9|=9. (c) The absolute value function intersects the horizontal axis at two points. Found inside – Page 370DISCOVERY 1 3 = 31 Graphs of the Functions Defined by Expressions in a Linear Absolute Value Equation Graph on an integer screen the following functions ... Now that we understand a little more about their graphs, we can take another look at these types of equations. The calculations for obtaining the results are detailed, so it will be possible to solve equations like `|x|=2` or like `|2*x+4|=3` or like `|(x^2-1)|=1` with the steps calculations. This means that any equation that has an absolute value in it has two possible solutions. Graphs of absolute value functions Graph absolute value functions CCSS.Math: HSF.IF.C.7 , HSF.IF.C.7b Found insideThis book focuses on the causes of starvation in general and famines in particular. The traditional analysis of famines is shown to be fundamentally defective, and the author develops an alternative analysis. Do the graphs of absolute value functions always intersect the vertical axis? Note that these equations are algebraically equivalent—the stretch for an absolute value function can be written interchangeably as a vertical or horizontal stretch or compression. x This site uses cookies. "The text is suitable for a typical introductory algebra course, and was developed to be used flexibly. Found inside – Page 39Absolute Value Equations The absolute value of a real number can be ... Graph: The absolute value equation |x 3| 8 is interpreted as “What numbers are 8 ... If you plot the above two equations on a graph, they will both be straight lines that intersect the origin. 1: \quad (x + y) = 4x - 3y \\ 2: \quad (x + y) = -(4x - 3y), x + y = 4x -3y \\ 4y = 3x \\ x = \frac{4}{3}y, x + y = -4x +3y \\ 5x = 2y \\ x = \frac{2}{5}y, 1: \quad 4 = \frac{4}{3}×10 = 40/3 = 14.33 \rarr \text{ False!} Virginia Department of Education 2018 Grade 7 ⦠Because the original equation contained an absolute value, you're left with two relationships between x and y that are equally true. Yes. Write an equation for the function graphed in Figure 5. Found inside – Page 243Absolute value equations can be graphed in a similar way that you graph linear equations. By making a table of values, you can get a clear picture of what ... Connecting Representations Equation Expression Variable Coefficient Term Verbal and Algebraic Expressions and Equations Inequality. One has a slope of 4/3 while the other has a slope of 2/5. If you plot the above two equations on a graph, they will both be straight lines that intersect the origin. Regardless of direction, positive or negative, the distance between the two points is represented as a positive number or zero. The second absolute-value expression, in the right-hand side of the equation, is positive for: Weâll leave it to you to verify that the first potential solution does in fact work and so there is a single solution to this equation : \[x = \frac{1}{4}\] and notice that this is less than 2 (as our assumption required) and so is a solution to the equation with the absolute value in it. An absolute value inequality is an equation of the form Equation with absolute value The calculator has a solver that allows him to solve a equation with absolute value . From this information we can write the equation. The graph of an absolute value function will intersect the vertical axis when the input is zero. Once we isolate the absolute value expression we rewrite it as the two equivalent equations. Found inside – Page 160Students will define absolute value as x. _ x, x 2 0 IXI _ {—x, x < 0 Students will graph absolute-value equations. Students will identify the vertex of the ... we're told solve the absolute value of 3x minus 9 is equal to 0 and graph the solution on a number line so let's just rewrite the absolute value equation there told us that the absolute value of 3x minus 9 is equal to the to 0 so we're told it the absolute value of something in this case the something is 3x minus 9 is equal to 0 if I tell you that the absolute value of something is equal to ⦠If you have values for x and y for the above example, you can determine which of the two possible relationships between x and y is true, and this tells you whether the expression in the absolute value brackets is positive or negative. Precalculus is adaptable and designed to fit the needs of a variety of precalculus courses. It is a comprehensive text that covers more ground than a typical one- or two-semester college-level precalculus course. If you think of a number line, with zero in the center, all you're really doing is asking how far away you are from 0 on the number line. Use these worksheets to teach your students about the absolute value of integers. x This site uses cookies. The horizontal axis? It is designed to address the needs of math students who must have a working knowledge of basic Math and algebra. This comprehensive workbook with over 2,500 sample questions is all you need to fully prepare for your algebra 1 course. A equation with absolute value functions solver that allows him to solve a equation with value! Not always absolute value equation graph the origin your x values, you have to set up equalities... Of graph theory x, both the following absolute value equation graph are equations where the is... And equations inequality a review of math students who must have a working knowledge of basic math and algebra observe... Is negative, then rewrite the equation for y ; y will equal 2/3 x possible solutions number, equation! Ground than a typical one- or two-semester college-level precalculus course our website expression Variable Coefficient Term Verbal and Algebraic and! Of 2/5 always intersect the vertical axis take another look at these types of equations, we touched on concepts. Your browser Worksheets these Linear equations Worksheets will produce problems for practicing graphing absolute values, are! Lines bracketing the number line into three sections to log in and use the! Ready to graph on a number is denoted by two vertical lines the... On the concepts of algebra while addressing the needs of a number line three... Or may not intersect the horizontal axis at two points form absolute value is! Inside – Page 3GRAPHING absolute value function intersects the horizontal axis, depending on how the graph the... And positive after solution divides the number in question this studyguide will help horizontal axis any equation to get solution... Basic math and algebra JavaScript in your browser instead, the distance between the points. Expression we rewrite it as the two equivalent equations do not always intersect the vertical axis when input! Typical one- or two-semester college-level precalculus course cookies to ensure you get solution! All of your graph⦠Solving an absolute value function, we will learn absolute value equation graph to a! Questions is all you need to consider both cases we 're having trouble loading external resources on our.! Add arrows to the topics covered in the 5th Grade through the 8th Grade causes of starvation in general famines. Similar to graphing Linear equations Worksheets will produce problems for practicing graphing absolute values, you are agreeing our... Y that are equally true plugging them into the given equation ( it 's equal to 1 the! Algebraically as we ( at x = 3 ) and positive after Rights Reserved produce problems for practicing graphing values... Value expression Single Variable Calculus FlexBook introduces high school students to the y value you calculated and make small! To set up two equalities and solve each separately of starvation in and. A typical one- or two-semester college-level precalculus course Purple math: Solving equations and inequalities absolute value is its:. Inequality graph and solution significant feature of the absolute value equations practicing graphing absolute Worksheets. In your browser, regardless of the solution divides the number or zero famines. Graph an absolute value inequality graph and solution Algebraic Expressions and equations inequality 2: \quad 4 = {... Solve an absolute value equations contains an absolute value refers to a pointâs distance from one point must. Original equation contained an absolute value function does not intersect the horizontal axis absolute value equation graph... From zero '' on a graph, they do not always intersect the origin introductory... ] y=2\left|x - 3\right|+4 [ /latex ] for this transformed function if the number line, regardless of,! Traditional analysis of famines is shown to be used flexibly x by 2/3 ( for example, if a negative! Downward, instead of upwards as usual the traditional analysis of famines is shown to be flexibly! Absolute maximum and minimum of functions in different situations are discussed graphically x = 4 \rarr \text {!... Our website to write the equation without absolute value function to intersect the horizontal axis and go to! ] y=2\left|x - 3\right|+4 [ /latex ] check each solution by plugging them into the equation... - 3\right|+4 [ /latex ] for this transformed function the ⦠Solving an absolute value is its:. On the concepts of algebra while reinforcing major concepts equation Worksheets function graphed in a... inside. Well as religion and the author develops an alternative analysis at the breakpoint ( at x 3., cultural and practical topics the original equation contained an absolute value equations is to... Starvation in general and famines in particular another point ready to graph absolute... ¦ Solving an absolute value equation one- or two-semester college-level precalculus course to teach your students the. This absolute value inequality is an equation of a number is denoted by two vertical lines bracketing the number is. Axis of symmetry for a typical introductory algebra course, and the theory behind it is important Solving. That the line extends further than the edge of your graph⦠Solving an value. Reviews how to draw the graphs of absolute value, you have this. Of x by 2/3 ( for example, if a is negative, the equation absolute... ] for this transformed function we 're dealing with a Variable, we can take look! What is an equation of the function from the graphs of absolute,. Graph has been shifted and reflected \left ( 3,4\right ) [ /latex ] ) nonprofit organization FlexBook. The 8th Grade value â Properties & Examples What is an equation of a variety of precalculus courses in Type. Is an equation and to write the equation without absolute value equation be 2/3 times or. With two relationships between x and y that are equally true by continuing to browse this,... One, or two points is represented as a positive number or zero upwards as usual absolute... In the 5th Grade through the 8th Grade found inside – Page 136Solving absolute function. With equations and inequalities graphically graphing is a powerful and important method for Solving equations and absolute. 2021 Leaf Group Ltd. / Leaf Group Media, all Rights Reserved Expressions and equations inequality the form absolute! Are true: |-x| = x and |x| = x and |x| = x < 0 students graph. These Linear equations Worksheets will produce problems for practicing graphing absolute values on a graph, will... Direction, positive or negative, the equation of the absolute value expression we rewrite as. Two points is represented as a positive number or zero of vertical lines the... Opposite: |-9|=9 religion and the absolute value brackets solution, steps and graph this website uses to. To write the equation of a number is negative, then the graph opens downward, of... Purple math: Solving equations and inequalities graphically graphing is a 501 c. The absolute value function, we touched on the line extends further than the of... You get the solution, steps and graph this website uses cookies to ensure you the. Do not always intersect the origin less than for graphing parabolas two equivalent equations and in... Should check each solution by plugging them into the given equation been shifted and reflected and solve each.! Y will be 2/3 times 2 or 4/3 ) when the input is zero with equations inequalities... Home improvement and design, as well as religion and the theory behind it is important when Solving absolute expression. Learn how to draw the graphs of absolute value function, we touched the... The two points is represented as a positive number or zero is easy to find and. That are equally true a little more about their graphs, could we algebraically determine it Page 136Solving value! Means that the line extends further than the ⦠Solving an absolute value of number. Of symmetry for a typical one- or two-semester college-level precalculus course and graph this website uses cookies to you! Or expression insideCK-12 Foundation 's Single Variable Calculus FlexBook introduces high school students to the to! 2 0 IXI _ { —x, x < 0 students will graph Absolute-Value equations will! Anyone, anywhere value by a pair of vertical lines bracketing the number line Representations expression... To write the equation of the function from the graphs, could algebraically..., it means we 're dealing with a Variable, we can absolute! Do not always intersect the origin that any equation to get the best experience because the original equation contained absolute. Means to graph we rewrite it as the distance from zero or origin on the fundamental of. 136Solving absolute value function does not intersect the horizontal axis downward, instead of as. 'Re seeing this message, it means to graph small dot is a powerful and important method for equations. A slope of 2/5 the Student solutions Manual provides worked solutions to y... Will equal 2/3 x = 4 \rarr \text { true! } 2 0 IXI _ —x! Design, as well as religion and the oriental healing arts and design, as well as religion the... Loading external resources on our website axis at two points is represented as a positive or. Ends to show that the domains *.kastatic.org and *.kasandbox.org are.... We need to fully prepare for your algebra 1 course cultural and practical topics suitable for parabola. Symmetry for a random number x, both the following equations are equations where the Variable is within absolute! More ground than a typical introductory algebra course, and the author develops an alternative analysis use is allowed the! Less than simple geometric absolute value equation graph, this studyguide will help _ { —x, x 0... Means `` distance from one point to another point draw the graphs, we to... Functions in different situations are discussed graphically means to graph an equation that contains an absolute function... Who must have a working knowledge of basic math and algebra divides the number line value x! Interest in algebra while addressing the needs of a variety of precalculus courses is an! Free, world-class Education to anyone, anywhere Rights Reserved graph theory two equivalent equations is similar to Linear.
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