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Devin attempted to solve the inequality -2x+6>10 following the steps below:

•subtract 6 from both sides of the inequality.
•divide both sides of the inequality by -2.

He finds that x>-2. Clearly explain why this is not a correct solution. In your response, be sure to explain what Devin needs to do to find the correct solution.

  • Algebra -

    multiplying or dividing by negative values changes the direction of the inequality. So, the answer is x < -2

    To see why this is so, work the problem without multiplying by negative values. In this case, that can be done as follows:

    -2x + 6 > 10
    subtract 6
    -2x > 4
    add 2x
    0 > 4 + 2x
    subtract 4
    -4 > 2x
    -2 > x

    see, multiplying by a negative is like swapping things to the other side and multiplying by a positive. So, the effective direction of the inequality changes.

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