Question

hidden message

1. work each exercise. all work must be shown on loose leaf.
2. shade in the block that contains the answer.
3. read the message in the unshaded blocks.

exercises
solve.

1. $2(3y + 4) = 32$ $y = 4$
2. $3(4y - 5) = 69$
3. $36 = 3(7t + 5)$
4. $156 = 4(6w - 9)$
5. $6x - (3x + 7) = 29$
6. $5m - (6m + 9) = 11$
7. $9m - (4m - 8) = 53$
8. $13x - (5x - 11) = -13$
9. $4(3x + 2) - 16 = 16$
10. $7(2x - 3) = 3(4x - 11)$
11. $6(5y + 7) = 7(4y - 10)$
12. $5(e + 6) = 4(e + 7)$
13. $9(x + 8) + 12 = 8(x + 8) + 10$
14. $18 - (3x + 5) = 5(x - 1) - 6$
15. $\frac{1}{3}(9x + 27) - 4 = \frac{1}{2}(2x + 54)$
16. $\frac{1}{5}(25x - 75) + 9 = \frac{1}{4}(8x + 36)$
17. $26 - (4x - 11) = -5(x + 7)$
18. $4(9y - 5) = 10(3y + 17) - 40$
19. $2(x - 13) = x - 31$
20. $5(x - 11) = 3x - 43$
21. $7(x + 1) = 2x + 57$
22. $5(x - 2) = -30$
23. $\frac{1}{7}(x + 21) = -6$
24. $2(x - 8) = -16 - 2$

Explanation:

Let's solve exercise 2: \( 3(4y - 5) = 69 \)

Step 1: Divide both sides by 3

To isolate the term with \( y \), we divide both sides of the equation by 3.
\( \frac{3(4y - 5)}{3} = \frac{69}{3} \)
Simplifying, we get \( 4y - 5 = 23 \)

Step 2: Add 5 to both sides

To isolate the term with \( y \), we add 5 to both sides of the equation.
\( 4y - 5 + 5 = 23 + 5 \)
Simplifying, we get \( 4y = 28 \)

Step 3: Divide both sides by 4

To solve for \( y \), we divide both sides of the equation by 4.
\( \frac{4y}{4} = \frac{28}{4} \)
Simplifying, we get \( y = 7 \)

Answer:

\( y = 7 \)