Question 1: Solve for x: 3x + 5 = 2x + 9.

Answer: 4

Question 2: Solve for y: 4(y - 2) = 2y + 6.

Answer: 6

Question 3: Solve for x: 5x - (x + 3) = 2x + 4.

Answer: 4

Question 4: Explain the mistake in solving the equation: 2x + 3 = x + 5, where someone subtracts 3 from both sides and then divides both sides by 2 without simplifying correctly.

Answer: They incorrectly divided after subtracting, ignoring that subtraction should be performed first to isolate the variable properly.

Question 5: Construct a multi-step equation with variables on both sides that simplifies to x = -2. Do not solve it.

Answer: Example: 4(x + 1) - 2x = 6 - x

Question 6: Identify the error in solving: x/2 + 3 = x/2 + 5. What is the correct approach?

Answer: The error is assuming the variable terms cancel; in fact, subtract the x/2 from both sides first, then solve.

Question 7: Solve for z: 2z + 4 = 3z - 2.

Answer: 6

Question 8: A common misconception is to cancel out variables across the equation. Identify this mistake in solving: 3x + 2 = 3x + 5.

Answer: They incorrectly cancel 3x from both sides, ignoring that 3x = 3x, which does not eliminate the variable here.

Question 9: Solve for y: 2(3y - 4) = y + 10.

Answer: 4

Question 10: A student solves 2x + 3 = x + 7 and gets x = 4. Identify their mistake and correct it.

Answer: They forgot to subtract x from both sides; correct steps: subtract x: x + 3 = 7; subtract 3: x = 4.

Question 11: Solve for x: 7x - 2(3x - 1) = 4x + 5.

Answer: 2