For the following problem, indicate the line where the mistake is (if any) and explain how it can be corrected. Be sure to include the correct answer. If there is no mistake, explain the general process for working the problem. Solve the following equation: 3x - 7 = 4(x + 3). The provided steps are: (1) 3x - 7 = 4(x + 3), (2) 3x - 7 = 4x + 12, (3) x - 7 = 12, (4) x = 19.

For the following problem, indicate the line where the mistake is (if any) and explain how it can be corrected. Be sure to include the correct answer. If there is no mistake, explain the general process for working the problem. Solve the following equation: 3x - 7 = 4(x + 3). The provided steps are: (1) 3x - 7 = 4(x + 3), (2) 3x - 7 = 4x + 12, (3) x - 7 = 12, (4) x = 19.

Answer

The mistake is in line (3). In line (2), the equation is 3x - 7 = 4x + 12. To move from line (2) to line (3), it appears the solver attempted to subtract 3x from both sides. However, 4x minus 3x equals 1x (or just x), which should remain on the right side of the equation. Subtracting 3x correctly results in: -7 = x + 12. To correct the mistake and solve the equation fully: 1) Start with 3x - 7 = 4(x + 3). 2) Distribute the 4: 3x - 7 = 4x + 12. 3) Subtract 3x from both sides to isolate the x term on one side: -7 = x + 12. 4) Subtract 12 from both sides to isolate x: -7 - 12 = x. 5) Simplify to find the final answer: x = -19. The correct answer is x = -19.