Solve and graph two-step inequalities

Answer Key - Grade 7 Math Worksheet - Building Confidence

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

1. 1.

   Luz works on 2x − 4 ≥ 10 and gets 2x ≥ 14 after the first step. What inequality gets x by itself?

   x ≥ 7
2. 2.

   Tala takes the first step of 5x + 5 < 30 and gets 5x < 25. What inequality gets x by itself?

   x < 5
3. 3.

   The math club warm-up is 3x + 6 ≥ 30, and Bo wants to finish first. What inequality gets x by itself?

   x ≥ 8
4. 4.

   Milo copies 4x − 4 > 16 from the board and draws the bars. What inequality gets x by itself?

   x > 5
5. 5.

   Ren gets -3x − 3 ≥ 9 as the bonus question. What inequality gets x by itself?

   x ≤ -4
6. 6.

   Esme solves 2x + 1 > 7 and draws the answer on a number line marked every 1. Which number line is right?

   • an open circle at 3, shaded to the left
   • a closed circle at 3, shaded to the right
   • an open circle at 3, shaded to the right
   • an open circle at 4, shaded to the right
7. 7.

   Noah solves -2x + 4 ≥ 10 and draws the answer on a number line marked every 1. Which number line is right?

   • a closed circle at -3, shaded to the right
   • a closed circle at -3, shaded to the left
   • a closed circle at -9, shaded to the left
   • an open circle at -3, shaded to the left
8. 8.

   Ari solves 3x − 6 < 9 and draws the answer on a number line marked every 1. Which number line is right?

   • an open circle at 9, shaded to the left
   • a closed circle at 5, shaded to the left
   • an open circle at 5, shaded to the right
   • an open circle at 5, shaded to the left
9. 9.

   Tala tests four numbers in 3x + 2 > 17. Which number makes it true?

   • 3
   • 6
   • 4
   • 5
10. 10.

    Pia has four guesses for 4x − 4 < 16, and only one works. Which number makes it true?

    • 6
    • 7
    • 4
    • 5