Question

20 POINTS~ 2/5 |5x+10| -14 > -6 Please explain both answers

Answer 1

Answer:

$x2$

Step-by-step explanation:

We have the inequality:

$\frac{2}{5}|5x+10|-14>-6$

First, we can factor out a 5 from our absolute value. This yields:

$\frac{2}{5}(5|x+2|)-14>-6$

Simplify:

$2|x+2|-14>-6$

Add 14 to both sides:

$2|x+2|>8$

Divide both sides by 2:

$|x+2|>4$

Definition of Absolute Value:

$x+2>4\text{ or } -(x+2)>4$

Solve each case individually:

Case 1:

$x+2>4$

Subtract 2 from both sides:

$x>2$

Case 2:

$-(x+2)>4$

Divide both sides by -1. Flip the sign:

$x+2$

Subtract 2 from both sides:

$x$

So, our answers are:

$x2$

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:

$x2$

And we're done!