Posted by **Nicole** on Friday, April 20, 2012 at 7:15pm.

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

â€¢subtract 6 from both sides of the inequality.

â€¢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 -
**Steve**, Saturday, April 21, 2012 at 6:02am
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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