Question

Mai solved the equation below incorrectly. Identify Mai's error and then solve the equation correctly.

(1/3)(1/2x - 9) = (1/2)(x + 18)
A. Mai incorrectly distributed the (1/3) and (1/2) terms. The correct solution is x = 48.
B. Mai incorrectly combined like terms. The correct solution is x = 42.
C. Mai incorrectly distributed the (1/3) and (1/2) terms. The correct solution is x = 54.
D. Mai incorrectly combined like terms. The correct solution is x = 36.

Answer 1

Mai's error in solving the equation was incorrect distribution. The correct solution is x = -9.

Step-by-step explanation:

Mai's error in solving the equation is that she incorrectly distributed the (1/3) and (1/2) terms. To solve the equation correctly, we need to distribute these terms correctly and then simplify the equation. Here are the steps:

1. Distribute (1/3) and (1/2) to their respective terms: (1/3)(1/2x - 9) = (1/2)(x + 18)
2. After distribution, the equation becomes: (1/6)x - 3 = (1/2)x + 9
3. Combine like terms: Subtract (1/6)x from both sides of the equation to isolate the variable. This gives us: -3-(1/6)x = (1/2)x + 9-(1/6)x
4. Simplify both sides of the equation: -3-(1/6)x = (7/6)x + 9
5. Combine like terms again: Add (7/6)x to both sides of the equation to eliminate the variable. This gives us: (-1/6)x - (7/6)x = 9 + 3
6. Simplify both sides of the equation: (-8/6)x = 12
7. Divide both sides of the equation by (-8/6) to solve for x: x = 12 / (-8/6)
8. Simplify the division: x = 12 * (-6/8)
9. Further simplification: x = -9

So, Mai's error was incorrect distribution, and the correct solution to the equation is x = -9.