Absolute value inequalities

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Ari solves |x - 3| < 6 on paper. What is the answer, written like 2 < x < 9?

   -3 < x < 9
2. 2.

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

   -9 ≤ x ≤ -3
3. 3.

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

   x < 2 or x > 6
4. 4.

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

   x ≤ -6 or x ≥ 4
5. 5.

   Milo solves |x - 8| > 3 on paper. What is the answer, written like x < 1 or x > 6?

   x < 5 or x > 11
6. 6.

   Ren wants to graph |x + 4| < 5 with a pencil. Which graph is right?

   • Closed circles at -9 and 1, shaded between
   • Open circles at -9 and 1, shaded outward
   • Open circles at -9 and 1, shaded between
   • Open circles at -5 and 5, shaded between
7. 7.

   Zee wants to graph |x + 3| ≤ 1 on paper. Which graph is right?

   • Closed circles at -4 and -2, shaded outward
   • Closed circles at -1 and 1, shaded between
   • Closed circles at -4 and -2, shaded between
   • Open circles at -4 and -2, shaded between
8. 8.

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

   • x < -3
   • No solution
   • x = -2
   • All real numbers
9. 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. 10.

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

    • No solution
    • All real numbers
    • x ≠ -3
    • x > -5