Answer:
[tex]x<-6\text{ or } x>2[/tex]
Step-by-step explanation:
We have the inequality:
[tex]\frac{2}{5}|5x+10|-14>-6[/tex]
First, we can factor out a 5 from our absolute value. This yields:
[tex]\frac{2}{5}(5|x+2|)-14>-6[/tex]
Simplify:
[tex]2|x+2|-14>-6[/tex]
Add 14 to both sides:
[tex]2|x+2|>8[/tex]
Divide both sides by 2:
[tex]|x+2|>4[/tex]
Definition of Absolute Value:
[tex]x+2>4\text{ or } -(x+2)>4[/tex]
Solve each case individually:
Case 1:
[tex]x+2>4[/tex]
Subtract 2 from both sides:
[tex]x>2[/tex]
Case 2:
[tex]-(x+2)>4[/tex]
Divide both sides by -1. Flip the sign:
[tex]x+2<-4[/tex]
Subtract 2 from both sides:
[tex]x<-6[/tex]
So, our answers are:
[tex]x<-6, x>2[/tex]
Since our inequality is a greater than, we will have an "or" inequality.
So, our answer is all values left to the first solution and all values to the right of the second solution:
[tex]x<-6\text{ or } x>2[/tex]
And we're done!
