Question 1: Solve for x: \( \frac{1}{2}x + 3 = 7 \).

Answer: 8

Question 2: Solve for y: \( 3y - \frac{2}{3} = 4 \).

Answer: 3

Question 3: Simplify: \( \frac{2}{3}x + \frac{4}{3} = 2x - 1 \).

Answer: x = 3

Question 4: Construct the equation and solve: If \( \frac{1}{4}x + 5 = \frac{3}{4}x - 2 \).

Answer: x = 14

Question 5: Multiply through to solve: \( \frac{2}{5}x - 1 = \frac{1}{5}x + 2 \).

Answer: 9

Question 6: A recipe requires \( \frac{3}{4} \) cup of sugar per batch. If you want to make enough for 5 batches, how much sugar do you need in total?

Answer: 3.75

Question 7: Solve: \( \frac{5}{6}x + 2 = \frac{1}{2}x + 4 \).

Answer: 6

Question 8: Using the multiply through method, solve for x: \( \frac{1}{3}x + \frac{2}{3} = \frac{2}{3}x - 1 \).

Answer: 3

Question 9: A painter charges \( \frac{1}{4} \) of their fee per wall. If their total fee is \( \$200 \), how many walls did they paint?

Answer: 4

Question 10: Identify and correct the mistake: \( \frac{2}{3}x + 4 = \frac{1}{3}x + 7 \) was solved as \( \frac{2}{3}x - \frac{1}{3}x = 7 - 4 \) but the answer was \( x = 9 \).

Answer: The mistake is subtracting \( \frac{1}{3}x \) from both sides; the correct step is to subtract \( \frac{1}{3}x \) from both sides, leading to \( \frac{1}{3}x + 4 = 7 \), then solving properly.