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Grade 9 · Math · Algebra 1

9th grade Absolute value inequalities worksheet

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Absolute value inequalities

Grade 9 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

  1. Esme solves |x - 7| < 2 in a math notebook. What is the answer, written like 2 < x < 9?

  2. Jun solves |x + 6| ≤ 3 on paper. What is the answer, written like 2 < x < 9?

  3. Kira solves |x - 4| > 2 with a pencil. What is the answer, written like x < 1 or x > 6?

  4. Luz solves |x + 1| ≥ 5 in a math notebook. What is the answer, written like x < 1 or x > 6?

  5. Noah solves |x + 7| ≥ 2 with a pencil. What is the answer, written like x < 1 or x > 6?

  6. Tala wants to graph |x - 5| > 1 in a math notebook. Which graph is right?

    • Open circles at -1 and 1, shaded outward
    • Open circles at 4 and 6, shaded outward
    • Open circles at 4 and 6, shaded between
    • Closed circles at 4 and 6, shaded outward

  7. Ari looks at |x + 2| < -1 on paper. What is the solution?

    • x = -2
    • All real numbers
    • No solution
    • x < -3

  8. Bo looks at |x - 5| ≥ -3 with a pencil. What is the solution?

    • All real numbers
    • No solution
    • x ≥ 2
    • x = 5

  9. Esme looks at |x - 4| < 0 in a math notebook. What is the solution?

    • No solution
    • x < 4
    • x = 4
    • All real numbers

  10. Jun looks at |x + 3| > -2 on paper. What is the solution?

    • No solution
    • x > -5
    • x ≠ -3
    • All real numbers
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9th grade Absolute value inequalities worksheet – printable
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About this worksheet

Absolute value inequalities. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can read |x - 3| < 4 as "x is less than 4 away from 3" and write the stretch -1 < x < 7.
  • I can clear the numbers around the bars, graph the answer, and write |x - c| < d from a graph or a story.

Standard: state-only (no CCSS standard names it)

Words to know

between (and): Close to the center: the stretch between the two ends.

beyond (or): Far from the center: the two pieces outside the ends.

no solution / all real numbers: A distance is never negative, so some inequalities fail or hold for every x.

Common mistakes

Your child read "less than" as "more than" or the other way round.

Your child measured the distance from 0 instead of from the center.

Your child used the wrong sign for the center.

What to say

Ask: is a number close to the center less than 4 away or more than 4 away?

Ask: in |x - 3| < 5, what number does the distance start from?

Ask: what value of x makes x + 2 equal 0?

Questions parents ask

What is the most common mistake with absolute value inequalities?

Your child read "less than" as "more than" or the other way round.

How can I help my child with absolute value inequalities?

Ask: is a number close to the center less than 4 away or more than 4 away?

Are these 9th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More algebra 1

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