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.

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

   x < 2
3. 3.

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

   x > 3
4. 4.

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

   x ≤ 7
5. 5.

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

   x ≥ 4
6. 6.

   Kira sees x with a minus in front: -x − 7 > 3. What inequality gets x by itself?

   x < -10
7. 7.

   Esme solves 3(x − 1) < 12 and draws the answer on a number line marked every 1. Which number line is right?

   • a closed circle at 5, shaded to the left
   • an open circle at 5, shaded to the left
   • an open circle at 5, shaded to the right
   • an open circle at 3, shaded to the left
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 -11, shaded to the left
   • an open circle at -6, shaded to the left
   • a closed circle at -6, shaded to the right
9. 9.

   Ari solves -x + 5 ≤ 2 and draws the answer on a number line marked every 1. Which number line is right?

   • an open circle at 3, shaded to the right
   • a closed circle at -7, shaded to the right
   • a closed circle at 3, shaded to the left
   • a closed circle at 3, shaded to the right
10. 10.

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

    • -6
    • -5
    • -3
    • -4