Absolute value inequalities

Answer Key - Grade 9 Math Worksheet - Building Confidence

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

1. 1.

   Ari reads |x - 3| < 4 on paper. Which sentence says the same thing?

   • x is less than 4 away from -3
   • x is less than 4 away from 0
   • x is more than 4 away from 3
   • x is less than 4 away from 3
2. 2.

   Bo reads |x - 5| > 2 with a pencil. Which sentence says the same thing?

   • x is more than 2 away from 5
   • x is more than 2 away from 0
   • x is less than 2 away from 5
   • x is more than 2 away from -5
3. 3.

   Esme reads |x + 2| ≤ 6 in a math notebook. Which sentence says the same thing?

   • x is at most 6 away from 0
   • x is at least 6 away from -2
   • x is at most 6 away from -2
   • x is at most 6 away from 2
4. 4.

   The solutions of |x - 3| = 4 are -1 and 7. Kira wants |x - 3| < 4 without bars. What is the answer, written like 2 < x < 9?

   -1 < x < 7
5. 5.

   The solutions of |x + 2| = 5 are -7 and 3. Luz wants |x + 2| ≤ 5 without bars. What is the answer, written like 2 < x < 9?

   -7 ≤ x ≤ 3
6. 6.

   The solutions of |x - 6| = 2 are 4 and 8. Milo wants |x - 6| > 2 without bars. What is the answer, written like x < 1 or x > 6?

   x < 4 or x > 8
7. 7.

   The solutions of |x + 1| = 3 are -4 and 2. Noah wants |x + 1| ≥ 3 without bars. What is the answer, written like x < 1 or x > 6?

   x ≤ -4 or x ≥ 2
8. 8.

   Pia tests numbers in |x - 2| < 3 on paper. Which number is a solution?

   • 4
   • 5
   • 8
   • -2
9. 9.

   Tala tests numbers in |x - 4| > 3 in a math notebook. Which number is a solution?

   • 2
   • 7
   • 6
   • 9
10. 10.

    Zee tests numbers in |x + 3| ≥ 5 on paper. Which number is a solution?

    • -1
    • -6
    • 4
    • 0