Solve and graph two-step inequalities

Answer Key - Grade 7 Math Worksheet

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

1. 1.

   Zee finds 4x + 1/2 > 5/2 in the math book's fraction corner. What inequality gets x by itself?

   x > 1/2
2. 2.

   Esme remembers the flip rule for -4x + 3 > 15. What inequality gets x by itself?

   x < -3
3. 3.

   Ari saves the hardest card, -2.5x + 5 < -10, for last. What inequality gets x by itself?

   x > 6
4. 4.

   Luz starts the quiz with 2x + 9 ≥ -5. What inequality gets x by itself?

   x ≥ -7
5. 5.

   Jun solves 2.5x − 1 > 4 and draws the answer on a number line marked every 0.5. Which number line is right?

   • a closed circle at 2, shaded to the right
   • an open circle at 2, shaded to the left
   • an open circle at 2, shaded to the right
   • an open circle at 5, shaded to the right
6. 6.

   Pia solves 4x + 1/2 ≤ 9/2 and draws the answer on a number line marked every 1/2. Which number line is right?

   • an open circle at 1, shaded to the left
   • a closed circle at 1, shaded to the left
   • a closed circle at 4, shaded to the left
   • a closed circle at 1, shaded to the right
7. 7.

   Bo solves -2x − 4 < 6 and draws the answer on a number line marked every 1. Which number line is right?

   • an open circle at 1, shaded to the right
   • an open circle at -5, shaded to the left
   • an open circle at -5, shaded to the right
   • a closed circle at -5, shaded to the right
8. 8.

   Milo tests four numbers in -3x + 4 < 7. Which number makes it true?

   • -3
   • 0
   • -2
   • -1
9. 9.

   Kira's study group has four numbers for 4x + 5 < -3. Which number makes it true?

   • -2
   • 0
   • -3
   • -1
10. 10.

    Ren checks four numbers in -1.5x + 3 > 12. Which number makes it true?

    • -4
    • -7
    • -5
    • -6