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.
2 x + 6 - 6 > 10 - 6
2x > 4 Divide both sides by - 2
Whenever you multiply or divide an inequality by a negative number, you must change the direction of the inequality.
In tis case :
( 2 x / - 2 ) < ( 4 / - 2 )
- x < - 2 Multiply both sides by - 1
You again must change the direction of the inequality:
x > 2
Devin's solution of x > -2 is not correct because he made an error during the second step of dividing both sides of the inequality by -2.
Let's go through the correct steps to find the solution:
Given inequality: -2x + 6 > 10
Step 1: Subtract 6 from both sides of the inequality:
-2x + 6 - 6 > 10 - 6
-2x > 4
Step 2: Divide both sides of the inequality by -2.
Important note: When dividing both sides of the inequality by a negative number, we need to switch the direction of the inequality sign. In this case, we divide by -2, so the inequality sign should change from greater than to less than.
-2x / -2 < 4 / -2
x < -2
Thus, the correct solution for the inequality -2x + 6 > 10 is x < -2.
To find the correct solution, Devin needs to divide both sides of the inequality by -2 and change the direction of the inequality sign from greater than to less than because he is dividing by a negative number. This is an important step to remember when solving inequalities.