Question

Anchara used the distributive property and the properties of equality to solve the equation 7 - 3(4 - 2x) = 4(x - 4) + 2x + 11, got the result -5 = -5 at her last step, and became confused. Did Anchara make a mistake in applying the properties? If so, describe the mistake and its significance, and tell how to correct it.

Answer 1

Anchara made a mistake in applying the properties of equality by subtracting 6x from both sides instead of subtracting 6x - 5. This led to an incorrect result of -5 = -5. To correct this mistake, subtract 6x - 5 from both sides of the equation.

Step-by-step explanation:

Anchara made a mistake in applying the properties of equality. Let's analyze the steps:

Step 1: Distribute the -3 and 4 on both sides of the equation:

7 - 12 + 6x = 4x - 16 + 2x + 11

Simplifying: 7 - 12 + 6x = 6x - 16 + 11

Step 2: Combine like terms:

-5 + 6x = 6x - 5

Step 3: Subtract 6x from both sides of the equation:

-5 = -5

At this last step, Anchara mistakenly subtracted 6x from both sides instead of subtracting 6x - 5. The significance of this mistake is that it led to an incorrect result of -5 = -5, which is a true statement but doesn't provide any meaningful solution to the equation. To correct this mistake, Anchara should subtract 6x - 5 from both sides of the equation. This will yield the correct solution.