Question

Andre and Diego were each trying to solve 2x+6=3x−8. Describe the first step they each make to the equation. The result of Andre's first step was -x+6=-8. The result of Diego's first step was 6=x−8.

Answer 1

Answer:

• Andre subtracted 3x from both sides
• Diego subtracted 2x from both sides

Step-by-step explanation:

Andre

Comparing the result of Andre's work with the original, we see that the "3x" term on the right is missing, and the x-term on the left is 3x less than it was. It is clear that Andre subtracted 3x from both sides of the equation.

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Diego

Comparing the result of Diego's work with the original, we see that the "2x" term on the left is missing, and the x-term on the right is 2x less than it was. It is clear that Diego subtracted 2x from both sides of the equation.

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Comment on their work

IMO, Diego has the right idea, as his result leaves the x-term with a positive coefficient. He can add 8 and he's finished, having found that x=14.

Andre can subtract 6 to isolate the variable term, and that will give him -x=-14. This requires another step to get to x=14. Sometimes minus signs get lost, so this would not be my preferred sequence of steps.

As a rule, I like to add the opposite of the variable term with the least (most negative) coefficient. This results in the variable having a positive coefficient, making errors easier to avoid.