# Writing absolute value equations from number lines

Ask the student to solve the equation and provide feedback. Examples of Student Work at this Level The student: You must reverse the inequality symbol when multiplying both sides of an inequality by a negative value: This means that any equation that has an absolute value in it has two possible solutions.

Examples of Student Work at this Level The student correctly writes and solves the first equation: Make sure the points increase in value from left to right. For example, represent the difference between x and 12 as x — 12 or 12 — x. To solve this, you have to set up two equalities and solve each separately.

Set Up Two Equations 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: How to Put an Absolute Value Equation or Inequality on a Number Line By Karl Wallulis; Updated April 24, Absolute value equations and inequalities add a twist to algebraic solutions, allowing the solution to be either the positive or negative value of a number.

A difference is described between two values. Isolate the variable in both inequalities to find the two solutions of the absolute value inequality.

Why is it necessary to use absolute value symbols to represent the difference that is described in the second problem? When you take the absolute value of a number, the result is always positive, even if the number itself is negative.

Should you use absolute value symbols to show the solutions? Emphasize that each expression simply means the difference between x and Draw solid lines visibly thicker than the number line to show the set of values that the variable can take.

If you plot the above two equations on a graph, they will both be straight lines that intersect the origin. This is solution for equation 1. Questions Eliciting Thinking Can you reread the first sentence of the second problem?

Sciencing Video Vault Isolate the variable in both equations to find the two solutions of the absolute value equation. For a random number x, both the following equations are true: In the example, label points -1, 0 and 7 on the number line from left to right.

Do you think you found all of the solutions of the first equation? Plug in known values to determine which solution is correct, then rewrite the equation without absolute value brackets. Wallulis holds a Bachelor of Arts in psychology from Whitman College.

Instructional Implications Provide feedback to the student concerning any errors made. Equation 2 is the correct one. Instructional Implications Model using absolute value to represent differences between two numbers.

Got It The student provides complete and correct responses to all components of the task. What is the difference? Graphing absolute value equations and inequalities is a more complex procedure than graphing regular equations because you have to simultaneously show the positive and negative solutions.

Plug these values into both equations. Draw a number line with 0 and the two points clearly labeled make sure the points increase in value from left to right. Absolute Value Equation Isolate the absolute value term in the equation by subtracting any constants and dividing any coefficients on the same side of the equation.

If needed, clarify the difference between an absolute value equation and the statement of its solutions. Absolute Value Inequality Isolate the absolute value term in the inequality by subtracting any constants and dividing any coefficients on the same side of the equation.

You can now drop the absolute value brackets from the original equation and write instead: Place a solid dot on the two points corresponding to the solutions of the equation found in Step 3 -- 3 and 7. Ask the student to consider these two solutions in the context of the problem to see if each fits the condition given in the problem i.

Finds only one of the solutions of the first equation. Simplify the process by splitting the equation or inequality into two separate solutions before graphing.

What are these two values?How To: Solve an absolute value equation and graph the answer on a number line By getexcellent; 8/11/10 AM Write and graph an equation in slope intercept form Plot absolute values on a number line How To: Graph a parabola.

Integers Math Absolute Value Equations Worksheets Absolute Value. To link to this page, copy the following code to your site. Split the equation into two separate equations: the first with the absolute value term removed, and the second with the absolute value term removed and multiplied by In the example, the two inequalities would be x + 3.

You can denote absolute value by a pair of vertical lines bracketing the number in question. When you take the absolute value of a number, the result is always positive, even if the number itself is negative.

The absolute number of a number a is written as $$\left | a \right |$$ And represents the distance between a and 0 on a number line. An absolute value equation is an equation that contains an absolute value expression. The equation $$\left | x \right |=a$$ Has two solutions x = a and x = -a because both numbers are at the distance a from 0.

Absolute Value Equations Discussion: Absolute value refers to the measure of distance from zero for any value on the number line. For example, the absolute value of 3 is 3 (written as) because there are three units between the number 3 and zero on the number line.

Writing absolute value equations from number lines
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