Solve and graph two-step inequalities

Answer Key - Grade 7 Math Worksheet - Challenge Me

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

1. 1.

   Esme meets a fraction in front of x: (2/3)x + 5 > 11. What inequality gets x by itself?

   x > 9
2. 2.

   Noah's puzzle of the week is (3/4)x − 2 ≤ 7. What inequality gets x by itself?

   x ≤ 12
3. 3.

   Ari tries (-2/5)x + 3 ≥ 7, which looks friendly but isn't. What inequality gets x by itself?

   x ≤ -10
4. 4.

   Jun divides first in 4(x − 2) ≤ 20. What inequality gets x by itself?

   x ≤ 7
5. 5.

   Pia spots a negative number outside the parentheses: -2(x + 3) < 10. What inequality gets x by itself?

   x > -8
6. 6.

   Milo starts the warm-up with -5x + 10 ≥ -15. What inequality gets x by itself?

   x ≤ 5
7. 7.

   Ren finishes the worksheet with 8x − 16 ≥ 24. What inequality gets x by itself?

   x ≥ 5
8. 8.

   Noah solves (-2/3)x + 2 ≥ 6 and draws the answer on a number line marked every 1. Which number line is right?

   • a closed circle at -6, shaded to the left
   • a closed circle at -6, shaded to the right
   • an open circle at -6, shaded to the left
   • a closed circle at -11, shaded to the left
9. 9.

   Luz tests four numbers in -3(x + 2) > 9. Which number makes it true?

   • -3
   • -6
   • -4
   • -5
10. 10.

    Tala's team has four numbers for 1.5x − 3 < 7.5. Which number makes it true?

    • 9
    • 8
    • 7
    • 6