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.
•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.
Answers
Steve
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.
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.