Absolute value equations

Answer Key - Grade 9 Math Worksheet

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

1. 1.

   Ari solves |x - 2| = 7 on paper. Which two numbers make it true, written with a comma between?

   -5, 9
2. 2.

   Bo solves |x + 2| = 6 with a pencil. Which two numbers make it true, written with a comma between?

   -8, 4
3. 3.

   Esme solves |x - 9| = 4 in a math notebook. Which two numbers make it true, written with a comma between?

   5, 13
4. 4.

   Jun solves |x + 5| = 1 on paper. Which two numbers make it true, written with a comma between?

   -6, -4
5. 5.

   Noah solves 5|x + 3| + 2 = 22 with a pencil. Which two numbers make it true, written with a comma between?

   -7, 1
6. 6.

   Ren looks at |x + 1| = -4 with a pencil. How many numbers solve it?

   • Two solutions
   • No solution
   • Infinitely many solutions
   • One solution
7. 7.

   Tala looks at 2|x| + 5 = 5 in a math notebook. How many numbers solve it?

   • Infinitely many solutions
   • Two solutions
   • No solution
   • One solution
8. 8.

   Ari marks -1 and 7 on a number line on paper. Which equation has exactly these two solutions?

   • |x - 3| = 8
   • |x - 3| = 4
   • |x + 3| = 4
   • |x - 4| = 3
9. 9.

   Bo marks 1 and 11 on a number line with a pencil. Which equation has exactly these two solutions?

   • |x - 6| = 10
   • |x - 6| = 5
   • |x + 6| = 5
   • |x - 5| = 6
10. 10.

    Esme marks -9 and -3 on a number line in a math notebook. Which equation has exactly these two solutions?

    • |x + 6| = 3
    • |x - 3| = 6
    • |x - 6| = 3
    • |x + 6| = 6