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.

   Jun does one step of 4x − 8 ≤ 12 very neatly and gets 4x ≤ 20. What inequality gets x by itself?

   x ≤ 5
3. 3.

   Pia finds this on a puzzle card: 2x + 4 < 16. What inequality gets x by itself?

   x < 6
4. 4.

   Kira spots a negative number in front of x: -2x + 6 < 14. What inequality gets x by itself?

   x > -4
5. 5.

   Esme solves 2x + 1 > 7 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
   • an open circle at 3, shaded to the right
   • an open circle at 3, shaded to the left
   • an open circle at 4, shaded to the right
6. 6.

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

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

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

   • 5
   • 3
   • 4
   • 6
8. 8.

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

   • -5
   • -6
   • -3
   • -4
9. 9.

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

   • 7
   • 4
   • 5
   • 6
10. 10.

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

    • -6
    • -3
    • -4
    • -5