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James was solving -2(7x - 8) = 30 and ended with x = 23/7. Here is his work.

1) Find his mistake and explain why it was a mistake. 2)Tell him how to correct the problem. 3)Make sure you give him the correct final answer. Use your words not AI.

(3 points)
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1 answer

Let's analyze James's work to find the mistake in his solution.

  1. Finding the mistake: When James solved the equation -2(7x - 8) = 30, he likely made an error during the distribution or when moving terms around. The correct steps for solving this equation involve first distributing the -2 to both terms inside the parentheses. If he arrived at x = 23/7, it suggests he might have incorrectly calculated or isolated x.

  2. How to correct the problem: To properly solve the equation, follow these steps:

    a) Distribute -2 across the terms inside the parentheses: \[ -2(7x) + (-2)(-8) = 30 \implies -14x + 16 = 30 \]

    b) Next, subtract 16 from both sides to isolate the term with x: \[ -14x = 30 - 16 \implies -14x = 14 \]

    c) Now, divide both sides by -14 to solve for x: \[ x = \frac{14}{-14} \implies x = -1 \]

  3. Correct final answer: The correct solution to the equation -2(7x - 8) = 30 is \( x = -1 \). Be careful during distribution and isolating variables, as those are common steps where mistakes can happen!