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.

   Milo spots 1.5x + 3 ≤ 12 on the decimal puzzle sheet. What inequality gets x by itself?

   x ≤ 6
2. 2.

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

   x > 1/2
3. 3.

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

   x < -3
4. 4.

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

   x > 6
5. 5.

   Tala solves -4x + 2 ≥ 14 and draws the answer on a number line marked every 1. Which number line is right?

   • a closed circle at -4, shaded to the left
   • a closed circle at -3, shaded to the right
   • an open circle at -3, shaded to the left
   • a closed circle at -3, shaded to the left
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 4, shaded to the left
   • a closed circle at 1, 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 -5, shaded to the right
   • an open circle at 1, shaded to the right
   • a closed circle at -5, shaded to the right
   • an open circle at -5, shaded to the left
8. 8.

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

   • -1
   • -2
   • -3
   • 0
9. 9.

   Zee narrows 4x − 3.5 > 2.5 down to four numbers, tapping the pencil on the desk. Which number makes it true?

   • 1.5
   • -0.5
   • 2.5
   • 0.5
10. 10.

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

    • -3
    • -1
    • -2
    • 0