Absolute value inequalities

Answer Key - Grade 9 Math Worksheet - Challenge Me

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

1. 1.

   Kira solves 2|x - 1| + 3 < 11 with a pencil. What is the answer, written like 2 < x < 9?

   -3 < x < 5
2. 2.

   Luz solves 3|x + 2| - 4 ≥ 5 in a math notebook. What is the answer, written like x < 1 or x > 6?

   x ≤ -5 or x ≥ 1
3. 3.

   Milo solves -2|x| + 1 > -7 on paper. What is the answer, written like 2 < x < 9?

   -4 < x < 4
4. 4.

   Noah solves -2|x - 1| + 3 ≥ -5 with a pencil. What is the answer, written like 2 < x < 9?

   -3 ≤ x ≤ 5
5. 5.

   Pia draws a graph on paper. Which absolute value inequality does the graph show?

   • |x + 3| ≤ 4
   • |x - 3| ≤ 4
   • |x - 3| ≤ 8
   • |x - 3| ≥ 4
6. 6.

   Ren draws a graph with a pencil. Which absolute value inequality does the graph show?

   • |x - 5| > 4
   • |x - 5| < 4
   • |x + 5| > 4
   • |x - 5| > 8
7. 7.

   Zee draws a graph on paper. Which absolute value inequality does the graph show?

   • |x + 4| ≥ 5
   • |x + 4| ≥ 10
   • |x - 4| ≥ 5
   • |x + 4| ≤ 5
8. 8.

   Ari's bean plant must grow to within 3 cm of 20 cm. Which inequality is right for h?

   • |h - 20| < 3
   • |h - 20| ≤ 3
   • |h - 3| ≤ 20
   • |h - 20| ≥ 3
9. 9.

   Bo's cake bakes best when the oven is within 10 degrees of 350. Which inequality is right for t?

   • |t - 350| ≤ 10
   • |t - 350| < 10
   • |t - 10| ≤ 350
   • |t - 350| ≥ 10
10. 10.

    Esme tells hikers to bring a water bottle if they are more than 6 miles from the water stop at mile 15. Which inequality is right for m?

    • |m - 15| > 6
    • |m - 15| < 6
    • |m - 15| ≥ 6
    • |m - 6| > 15