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.

   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.

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

   x ≤ 5
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 3, shaded to the left
   • an open circle at 5, shaded to the left
   • an open circle at 5, shaded to the right
8. 8.

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

   • a closed 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
   • an open circle at 3, shaded to the right
9. 9.

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

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

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

    • -2
    • -4
    • -5
    • -3