MIA · Mixed set · Unit 4

1. 1.

   Expand 6(x + (−5)).

   Answer. 6x + −30

   Distribute: 6x + 6(−5) = 6x + −30.

2. 2.

   A square has side x + 6. Write an expression for the perimeter.

   Answer. 4x + 24

   P = 4(x + 6) = 4x + 24.

3. 3.

   The equation 2x + 1 = 13 is true when x = 6. Check by substitution.

   Answer. checks (13 = 13)

   2(6) + 1 = 12 + 1 = 13.

4. 4.

   Solve 5x + 4 = 24.

   Answer. x = 4

   Subtract 4: 5x = 20. Divide by 5: x = 4.

5. 5.

   Solve 4x + 4 > 20. Then Ava needs 3 of that amount. What is the total they need?

   Answer. x > 12

   Subtract 4: 4x > 16. Divide by 4: x > 4. Then multiply by 3: x > 12.

6. 6.

   Expand 3(x + (−3)). Then Nora needs 3 of that amount. What is the total they need?

   Answer. 9x + −9

   Distribute: 3x + 3(−3) = 3x + −9. Then multiply by 3: 9x + −9.

7. 7.

   A square has side x + 9. Write an expression for the perimeter. Then Grace needs 5 of that amount. What is the total they need?

   Answer. 20x + 36

   P = 4(x + 9) = 4x + 36. Then multiply by 5: 20x + 36.

8. 8.

   The equation 2x + 4 = 20 is true when x = 8. Check by substitution. Then Sam needs 4 of that amount. What is the total they need?

   Answer. checks (80 = 20)

   2(8) + 4 = 16 + 4 = 20. Then multiply by 4: checks (80 = 20).

9. 9.

   Solve 2x + 8 = 12. Write a complete answer — Mei will compare with a partner.

   Answer. x = 2

   Subtract 8: 2x = 4. Divide by 2: x = 2.

10. 10.

    Solve 3x + 6 > 24. Then Theo needs 5 of that amount. What is the total they need?

    Answer. x > 30

    Subtract 6: 3x > 18. Divide by 3: x > 6. Then multiply by 5: x > 30.

11. 11.

    Think

    Nora tried this problem:
    Expand 2(x + (−3)).
    Nora wrote 4x + −6. That is not correct. What is the right answer?

    Answer. 2x + −6

    Nora’s answer 4x + −6 is off. Distribute: 2x + 2(−3) = 2x + −6.

12. 12.

    Think

    Owen tried this problem:
    A square has side x + 6. Write an expression for the perimeter.
    Owen wrote -4x + 24. That is not correct. What is the right answer?

    Answer. 4x + 24

    Owen’s answer -4x + 24 is off. P = 4(x + 6) = 4x + 24.

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