Question

An equation and the steps to solve it are shown below: 3x minus one over five times the quantity 10x plus 5 equals 6 Step 1: 3x – 2x – 1 = 6 Step 2: x – 1 = 6 Step 3: x – 1 – 1 = 6 – 1 Step 4: x = 5 In which step was the error made and why?

Answer 1

Answer:

either of Step 3 or Step 4

Step-by-step explanation:

At Step 3, -1 is added to both sides of the equation. Technically, this is correct (not an error), but it does not lead to a solution to the equation (so, could be considered to be an error). Adding +1 to both sides of the equation would lead more directly to a solution.

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At Step 4, x -1 -1 is simplified to x. This is an error, as the correct simplification is x-2, so the equation after this step should read x-2 = 5. If Step 3 had been executed by adding +1 to both sides of the equation, then the simplification here would be x=7.

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Answering "why" someone does something is always tricky. One can project one's own interpretation onto the actions of others, but one never really knows whether that is accurate or not.

The "why" in this case could go back to the motivation of the problem's author, which may be to see if the student can recognize that the opposite of -1 is +1, or that the sum -1-1 is not zero.

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My guess is that Step 3 is considered to be the erroneous step, and that choosing Step 4 will get you into a losing argument with your grader.