Multi-step inequalities: solve, graph and write from a story

Answer Key - Grade 8 Math Worksheet - Building Confidence

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

1. 1.

   Ari takes 2x off both bars of 5x + 2 > 2x + 14 and gets 3x + 2 > 14. What inequality gets x by itself?

   x > 4
2. 2.

   Bo takes x off both bars of 4x - 3 ≤ x + 12 and gets 3x - 3 ≤ 12. What inequality gets x by itself?

   x ≤ 5
3. 3.

   Esme takes 2x off both bars of 6x + 1 ≥ 2x + 25 and gets 4x + 1 ≥ 25. What inequality gets x by itself?

   x ≥ 6
4. 4.

   Kira solves 3x + 5 ≤ x + 13 and draws the answer on a number line marked every 1 from 0 to 10. Which picture is right?

   • a closed circle at 4, shaded to the left
   • an open circle at 4, shaded to the left
   • an open circle at 4, shaded to the right
   • a closed circle at 4, shaded to the right
5. 5.

   Luz solves 4x + 1 > 2x + 11 and draws the answer on a number line marked every 1 from 0 to 10. Which picture is right?

   • a closed circle at 5, shaded to the left
   • a closed circle at 5, shaded to the right
   • an open circle at 5, shaded to the left
   • an open circle at 5, shaded to the right
6. 6.

   Milo solves 5x - 2 ≥ 3x + 12 and draws the answer on a number line marked every 1 from 0 to 10. Which picture is right?

   • a closed circle at 7, shaded to the right
   • an open circle at 7, shaded to the right
   • a closed circle at 7, shaded to the left
   • an open circle at 7, shaded to the left
7. 7.

   Noah solves 2x + 9 < x + 16 and draws the answer on a number line marked every 1 from 0 to 10. Which picture is right?

   • an open circle at 7, shaded to the right
   • a closed circle at 7, shaded to the left
   • an open circle at 7, shaded to the left
   • a closed circle at 7, shaded to the right
8. 8.

   Ren tests four numbers in 4x + 1 < 2x + 9. Which number is a solution?

   • 3
   • 5
   • 4
   • 6
9. 9.

   Tala tests four numbers in 5x - 6 > 2x + 9. Which number is a solution?

   • 7
   • 3
   • 5
   • 4
10. 10.

    Zee tests four numbers in 3x + 2 ≥ x + 12. Which number is a solution?

    • 5
    • 3
    • 4
    • 2