UA · Unit 4 review

1. 1.

   Expand 5(x + (−1)).

   Answer. 5x + −5

   Distribute: 5x + 5(−1) = 5x + −5.

2. 2.

   A square has side x + 9. Write an expression for the perimeter.

   Answer. 4x + 36

   P = 4(x + 9) = 4x + 36.

3. 3.

   The equation 5x + 6 = 16 is true when x = 2. Check by substitution.

   Answer. checks (16 = 16)

   5(2) + 6 = 10 + 6 = 16.

4. 4.

   Solve 4x + 7 = 27.

   Answer. x = 5

   Subtract 7: 4x = 20. Divide by 4: x = 5.

5. 5.

   Solve 5x + 7 > 32. Then Nora needs 2 of that amount. What is the total they need?

   Answer. x > 10

   Subtract 7: 5x > 25. Divide by 5: x > 5. Then multiply by 2: x > 10.

6. 6.

   Expand 5(x + (−5)). Then Jonah needs 4 of that amount. What is the total they need?

   Answer. 20x + −25

   Distribute: 5x + 5(−5) = 5x + −25. Then multiply by 4: 20x + −25.

7. 7.

   A square has side x + 5. Write an expression for the perimeter. Then Priya needs 2 of that amount. What is the total they need?

   Answer. 8x + 20

   P = 4(x + 5) = 4x + 20. Then multiply by 2: 8x + 20.

8. 8.

   The equation 3x + 5 = 11 is true when x = 2. Check by substitution. Then Nora needs 2 of that amount. What is the total they need?

   Answer. checks (22 = 11)

   3(2) + 5 = 6 + 5 = 11. Then multiply by 2: checks (22 = 11).

9. 9.

   Solve 2x + 7 = 25. Write a complete answer — Owen will compare with a partner.

   Answer. x = 9

   Subtract 7: 2x = 18. Divide by 2: x = 9.

10. 10.

    Solve 3x + 4 > 16. Then Elena needs 5 of that amount. What is the total they need?

    Answer. x > 20

    Subtract 4: 3x > 12. Divide by 3: x > 4. Then multiply by 5: x > 20.

11. 11.

    Think

    Priya tried this problem:
    Expand 4(x + (−5)).
    Priya wrote 5x + −20. That is not correct. What is the right answer?

    Answer. 4x + −20

    Priya’s answer 5x + −20 is off. Distribute: 4x + 4(−5) = 4x + −20.

12. 12.

    Think

    Priya tried this problem:
    A square has side x + 5. Write an expression for the perimeter.
    Priya wrote 3x + 20. That is not correct. What is the right answer?

    Answer. 4x + 20

    Priya’s answer 3x + 20 is off. P = 4(x + 5) = 4x + 20.

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