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.

   Ari starts 3x + 3 > 21 and gets 3x > 18 after the first step. What inequality gets x by itself?

   x > 6
2. 2.

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

   x ≥ 7
3. 3.

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

   x < 5
4. 4.

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

   x > 5
5. 5.

   Zee's quiz starts with 5x − 5 ≤ 20. What inequality gets x by itself?

   x ≤ 5
6. 6.

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

   x ≤ -4
7. 7.

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

   Jun checks four numbers in -2x + 2 < 10 before class. Which number makes it true?

   • -5
   • -3
   • -4
   • -6
9. 9.

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

   • 5
   • 4
   • 6
   • 7
10. 10.

    Bo picks four numbers for -2x − 3 > 7, and only one works. Which number makes it true?

    • -6
    • -3
    • -5
    • -4