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9th grade · Math · Unit 18 of 18

Absolute Value Equations

Distance from a number, both ways

What your child practices

Solving one-variable equations and inequalities with absolute value, reading |x − a| as the distance from a, and writing absolute-value inequalities for real tolerances. Absolute value equations are a California addition to Algebra I.

California Content Standards learning standard: A-REI.3.1; A-CED.1 · solving and creating one-variable equations and inequalities involving absolute value

How we explain it

Children can open this short lesson before they practice.

  1. |x − a| is the distance between x and a on the number line.
  2. |x − a| = b means x − a = b or x − a = −b, so there are two answers (none if b is negative).
  3. |x − a| < b means x is between a − b and a + b. |x − a| > b means x is outside them.

Example: Solve |x − 3| = 5. x − 3 = 5, so x = 8. x − 3 = −5, so x = −2. Answer: x = −2 or x = 8

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    How many solutions does |x + 2| = 0 have?

    • No solution
    • One solution
    • Two solutions
    • Infinitely many

  2. Question 2

    What is |4 − 1|?

    • 6
    • 2
    • 4
    • 3

  3. Question 3

    A bolt should be 40 millimeters long, with a tolerance of 2 millimeters. Which inequality shows the allowed lengths L?

    • |L − 40| ≤ 2
    • |L − 2| ≤ 40
    • |L − 40| ≥ 2
    • |L + 40| ≤ 2

  4. Question 4

    Solve |2x − 10| = 4.

    |2x − 10| = 4

    • x = 7 only
    • x = 9 or x = 1
    • No solution
    • x = 3 or x = 7

  5. Question 5

    Solve |x + 3| = 3.

    |x + 3| = 3

    • x = −6 or x = 0
    • x = 6 or x = 0
    • x = 0 only
    • x = −6 only

  6. Question 6

    Solve |x − 3| < 8.

    • −5 < x < 11
    • x < −5 or x > 11
    • −8 < x < 8
    • x < 11

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