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 - 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
-2x > 4
0 > 4 + 2x
-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.