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How to Write an Absolute Value Inequality to Represent a Graph

Absolute value indicates a number's distance from zero on the number line. In mathematical notation, the absolute value of x is written by putting a vertical line on both sides of the x: I x I. By looking at a number line graph, you can write an inequality relating to absolute value.

Things You'll Need

  • Pen or pencil
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Instructions

    • 1

      Set up a number line graph. Draw a horizontal line and put a short vertical line in the middle. Label this line "0," then draw arrows on both ends of the line. Then, make short vertical lines out in both directions from zero. Lines to the right indicate positive integers; ones on the left indicate negative integers.

    • 2

      Draw and fill in dots at the points 4 and -4. Then, connect them with a solid line along the number line.

      The inequality here is "I x I is less than or equal to 4." To write a "less than or equal to" sign, write the "<" sign with a line beneath it.

    • 3

      Draw circles at the points 2 and -2, but do not fill them in. Then, draw a line from the "2" circle all the way out to the right arrow, and another line from the "-2" circle all the way out to the left arrow. The inequality here is I x I > 2. Because the points have circles instead of dots, they are not included in the solution, as was the case in Step 2.

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