L26 · One-variable inequalities

1. 1.

   Solve 8x ≤ 88. Write the inequality for x.

   Answer. x ≤ 11

   Divide both sides by 8 (positive, so the inequality direction stays): x ≤ 11.

2. 2.

   Solve 6x ≥ 66. Write the inequality for x.

   Answer. x ≥ 11

   Divide both sides by 6 (positive, so the inequality direction stays): x ≥ 11.

3. 3.

   Solve 4x ≤ 12. Write the inequality for x.

   Answer. x ≤ 3

   Divide both sides by 4 (positive, so the inequality direction stays): x ≤ 3.

4. 4.

   Solve 5x ≥ 20. Write the inequality for x.

   Answer. x ≥ 4

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

5. 5.

   Solve 6x ≤ 18. Write the inequality for x. Then Theo needs 4 of that amount. What is the total they need?

   Answer. x ≤ 12

   Divide both sides by 6 (positive, so the inequality direction stays): x ≤ 3. Then multiply by 4: x ≤ 12.

6. 6.

   Solve 3x ≤ 30. Write the inequality for x. Then Grace needs 2 of that amount. What is the total they need?

   Answer. x ≤ 20

   Divide both sides by 3 (positive, so the inequality direction stays): x ≤ 10. Then multiply by 2: x ≤ 20.

7. 7.

   Solve 4x ≤ 12. Write the inequality for x. Then Malik needs 3 of that amount. What is the total they need?

   Answer. x ≤ 9

   Divide both sides by 4 (positive, so the inequality direction stays): x ≤ 3. Then multiply by 3: x ≤ 9.

8. 8.

   Solve 2x > 18. Write the inequality for x. Then Priya needs 4 of that amount. What is the total they need?

   Answer. x > 36

   Divide both sides by 2 (positive, so the inequality direction stays): x > 9. Then multiply by 4: x > 36.

9. 9.

   Solve 2x < 12. Write the inequality for x. Then Theo needs 4 of that amount. What is the total they need?

   Answer. x < 24

   Divide both sides by 2 (positive, so the inequality direction stays): x < 6. Then multiply by 4: x < 24.

10. 10.

    Solve 3x > 27. Write the inequality for x. Then Theo needs 4 of that amount. What is the total they need?

    Answer. x > 36

    Divide both sides by 3 (positive, so the inequality direction stays): x > 9. Then multiply by 4: x > 36.

11. 11.

    Think

    Grace tried this problem:
    Solve 4x > 44. Write the inequality for x.
    Grace wrote x > 10. That is not correct. What is the right answer?

    Answer. x > 11

    Grace’s answer x > 10 is off. Divide both sides by 4 (positive, so the inequality direction stays): x > 11.

12. 12.

    Think

    Owen tried this problem:
    Solve 8x ≥ 88. Write the inequality for x.
    Owen wrote x ≥ 12. That is not correct. What is the right answer?

    Answer. x ≥ 11

    Owen’s answer x ≥ 12 is off. Divide both sides by 8 (positive, so the inequality direction stays): x ≥ 11.

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