Question

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.

Answer 1

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.