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.

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

   x ≤ 12
2. 2.

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

   x ≤ -10
3. 3.

   Luz finds (5/4)x + 1/2 < 3 in the challenge corner of the math book. What inequality gets x by itself?

   x < 2
4. 4.

   Tala sees parentheses in 3(x + 4) > 21. What inequality gets x by itself?

   x > 3
5. 5.

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

   x ≤ 7
6. 6.

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

   x > -8
7. 7.

   Bo reads 2.5(x + 2) ≥ 15 from the puzzle corner. What inequality gets x by itself?

   x ≥ 4
8. 8.

   Esme solves 3(x − 1) < 12 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 3, shaded to the left
   • a closed circle at 5, shaded to the left
   • an open circle at 5, shaded to the left
9. 9.

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

   • 9
   • 7
   • 8
   • 6
10. 10.

    Jun checks four numbers for (-2/3)x + 3 < 5. Which number makes it true?

    • -2
    • -4
    • -3
    • -5