Prep · One-variable inequalities

1. 1.

   Solve 7x ≤ 70. Write the inequality for x.

   Answer. x ≤ 10

   Divide both sides by 7 (positive, so the inequality direction stays): x ≤ 10.

2. 2.

   Solve 5x > 15. Write the inequality for x.

   Answer. x > 3

   Divide both sides by 5 (positive, so the inequality direction stays): x > 3.

3. 3.

   Solve 5x ≥ 35. Write the inequality for x.

   Answer. x ≥ 7

   Divide both sides by 5 (positive, so the inequality direction stays): x ≥ 7.

4. 4.

   Solve 7x ≤ 49. Write the inequality for x.

   Answer. x ≤ 7

   Divide both sides by 7 (positive, so the inequality direction stays): x ≤ 7.

5. 5.

   Solve 8x ≥ 72. Write the inequality for x. Then Priya needs 5 of that amount. What is the total they need?

   Answer. x ≥ 45

   Divide both sides by 8 (positive, so the inequality direction stays): x ≥ 9. Then multiply by 5: x ≥ 45.

6. 6.

   Solve 6x > 42. Write the inequality for x. Then Ava needs 2 of that amount. What is the total they need?

   Answer. x > 14

   Divide both sides by 6 (positive, so the inequality direction stays): x > 7. Then multiply by 2: x > 14.

7. 7.

   Solve 7x > 42. Write the inequality for x. Then Luis needs 2 of that amount. What is the total they need?

   Answer. x > 12

   Divide both sides by 7 (positive, so the inequality direction stays): x > 6. Then multiply by 2: x > 12.

8. 8.

   Solve 8x ≤ 32. Write the inequality for x. Then Sam needs 2 of that amount. What is the total they need?

   Answer. x ≤ 8

   Divide both sides by 8 (positive, so the inequality direction stays): x ≤ 4. Then multiply by 2: x ≤ 8.

9. 9.

   Solve 5x ≤ 50. Write the inequality for x. Then Luis needs 5 of that amount. What is the total they need?

   Answer. x ≤ 50

   Divide both sides by 5 (positive, so the inequality direction stays): x ≤ 10. Then multiply by 5: x ≤ 50.

10. 10.

    Solve 8x ≥ 32. Write the inequality for x. Then Owen needs 5 of that amount. What is the total they need?

    Answer. x ≥ 20

    Divide both sides by 8 (positive, so the inequality direction stays): x ≥ 4. Then multiply by 5: x ≥ 20.

11. 11.

    Think

    Mei tried this problem:
    Solve 5x > 60. Write the inequality for x.
    Mei wrote x > -12. That is not correct. What is the right answer?

    Answer. x > 12

    Mei’s answer x > -12 is off. Divide both sides by 5 (positive, so the inequality direction stays): x > 12.

12. 12.

    Think

    Nora tried this problem:
    Solve 3x < 15. Write the inequality for x.
    Nora wrote x < -5. That is not correct. What is the right answer?

    Answer. x < 5

    Nora’s answer x < -5 is off. Divide both sides by 3 (positive, so the inequality direction stays): x < 5.

Original extra practice. Keys are computed from the items, not guessed.