17. $7.8y - 4.9 = 5.4y + 2.3$
18. $2a - 9.3 = 0.8a + 5.1$
19. $13b + 3 = 19 + 9b$
20. $3x + 0.5(10x - 6) = 21$
21. $4(x + 2) - 2(x - 4) = 32$
22. $5(2 - 3y) + 9y = 4(3 - 2y)$
23. $6z^2 = 216$
24. $p^2 - 7 = 57$

Question

Accepted Answer

Let's solve each equation one by one:

### Problem 17: $ 7.8y - 4.9 = 5.4y + 2.3 $
# Explanation:
## Step 1: Subtract $ 5.4y $ from both sides
$ 7.8y - 5.4y - 4.9 = 5.4y - 5.4y + 2.3 $
$ 2.4y - 4.9 = 2.3 $
## Step 2: Add $ 4.9 $ to both sides
$ 2.4y - 4.9 + 4.9 = 2.3 + 4.9 $
$ 2.4y = 7.2 $
## Step 3: Divide both sides by $ 2.4 $
$ y = \frac{7.2}{2.4} $
$ y = 3 $
# Answer: $ y = 3 $

### Problem 18: $ 2a - 9.3 = 0.8a + 5.1 $
# Explanation:
## Step 1: Subtract $ 0.8a $ from both sides
$ 2a - 0.8a - 9.3 = 0.8a - 0.8a + 5.1 $
$ 1.2a - 9.3 = 5.1 $
## Step 2: Add $ 9.3 $ to both sides
$ 1.2a - 9.3 + 9.3 = 5.1 + 9.3 $
$ 1.2a = 14.4 $
## Step 3: Divide both sides by $ 1.2 $
$ a = \frac{14.4}{1.2} $
$ a = 12 $
# Answer: $ a = 12 $

### Problem 19: $ 13b + 3 = 19 + 9b $
# Explanation:
## Step 1: Subtract $ 9b $ from both sides
$ 13b - 9b + 3 = 19 + 9b - 9b $
$ 4b + 3 = 19 $
## Step 2: Subtract $ 3 $ from both sides
$ 4b + 3 - 3 = 19 - 3 $
$ 4b = 16 $
## Step 3: Divide both sides by $ 4 $
$ b = \frac{16}{4} $
$ b = 4 $
# Answer: $ b = 4 $

### Problem 20: $ 3x + 0.5(10x - 6) = 21 $
# Explanation:
## Step 1: Distribute $ 0.5 $
$ 3x + 5x - 3 = 21 $
## Step 2: Combine like terms
$ 8x - 3 = 21 $
## Step 3: Add $ 3 $ to both sides
$ 8x - 3 + 3 = 21 + 3 $
$ 8x = 24 $
## Step 4: Divide both sides by $ 8 $
$ x = \frac{24}{8} $
$ x = 3 $
# Answer: $ x = 3 $

### Problem 21: $ 4(x + 2) - 2(x - 4) = 32 $
# Explanation:
## Step 1: Distribute $ 4 $ and $ -2 $
$ 4x + 8 - 2x + 8 = 32 $
## Step 2: Combine like terms
$ 2x + 16 = 32 $
## Step 3: Subtract $ 16 $ from both sides
$ 2x + 16 - 16 = 32 - 16 $
$ 2x = 16 $
## Step 4: Divide both sides by $ 2 $
$ x = \frac{16}{2} $
$ x = 8 $
# Answer: $ x = 8 $

### Problem 22: $ 5(2 - 3y) + 9y = 4(3 - 2y) $
# Explanation:
## Step 1: Distribute $ 5 $ and $ 4 $
$ 10 - 15y + 9y = 12 - 8y $
## Step 2: Combine like terms
$ 10 - 6y = 12 - 8y $
## Step 3: Add $ 8y $ to both sides
$ 10 + 2y = 12 $
## Step 4: Subtract $ 10 $ from both sides
$ 2y = 2 $
## Step 5: Divide both sides by $ 2 $
$ y = \frac{2}{2} $
$ y = 1 $
# Answer: $ y = 1 $

### Problem 23: $ 6z^2 = 216 $
# Explanation:
## Step 1: Divide both sides by $ 6 $
$ z^2 = \frac{216}{6} $
$ z^2 = 36 $
## Step 2: Take square root of both sides
$ z = \pm\sqrt{36} $
$ z = \pm 6 $
# Answer: $ z = \pm 6 $

### Problem 24: $ p^2 - 7 = 57 $
# Explanation:
## Step 1: Add $ 7 $ to both sides
$ p^2 = 57 + 7 $
$ p^2 = 64 $
## Step 2: Take square root of both sides
$ p = \pm\sqrt{64} $
$ p = \pm 8 $
# Answer: $ p = \pm 8 $

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QUESTION IMAGE

Question

Explanation:

Problem 17: \( 7.8y - 4.9 = 5.4y + 2.3 \)

Step 1: Subtract \( 5.4y \) from both sides

Step 2: Add \( 4.9 \) to both sides

Step 3: Divide both sides by \( 2.4 \)

Step 1: Subtract \( 0.8a \) from both sides

Step 2: Add \( 9.3 \) to both sides

Step 3: Divide both sides by \( 1.2 \)

Step 1: Subtract \( 9b \) from both sides

Step 2: Subtract \( 3 \) from both sides

Step 3: Divide both sides by \( 4 \)

Answer:

Problem 18: \( 2a - 9.3 = 0.8a + 5.1 \)