# Algebra

posted by .

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 -

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
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.

## Similar Questions

1. ### algebra

7/11 - 2x < 3/10; {1/2, 1/3, 1/4, 1/5, 1/6} Rearrange the inequality to get add 2x to both sides 7/11 < 3/10 +2x subtract 3/10 from both sides 7/11 - 3/10 < 2x divide by both sides 2 (1/2)(7/11 - 3/10) < x Can you finish …
2. ### Pre-Algebra

inequality 0.75x>3 Multiply both sides of the inequality by 4/3 if you want to know what x is. from where did you get 4/3 to multiply to find x. How do you know that?
3. ### Algebra 2

-2/3x + 3<11 how do i solve this equation Subtract 3 from both sides. Then, multiply both sides by -(3/2) to get x alone. But whenever you have and inequality and multiply or divide by negative number, make sure to CHANGE THE DIRECTION …

Solve the inequality x > 6x - 10 and write a description of the graph. Show all work Subtracting x from both sides does not change the inequality sign direction. 0 > 5x - 10 Add 10 to both sides 5x < 10 Divide both sides by …

Directions:Solve and explain the inequality using words.Tell which wa shading goes. Problem: x+3=>2x+1 and -4x<-8 -4x<-8 The first inequality can be rewritten x <= 2 In words, x is less than or equal to 2. You can get that …
6. ### algebra

Why does the inequality sign change when both sides are multiplied or divided by a negative number?
7. ### Algebra

1. Why does the inequality sign change when both sides of the inequality are multiplied or divided by a negative number?
8. ### Algebra

1. Why does the inequality sign change when both sides of the inequality are multiplied or divided by a negative number?
9. ### algebra

Why does the inequality sign change when both sides are multiplied or divided by a negative number?