Question

Solve and graph the absolute value inequality: |2x + 4| > 8

Answer 1

The thing to keep in mind about about absolute value expressions is that abs value is simply the DISTANCE from 0.

So |{something}|>8 means that the {something} (whatever is INSIDE the abs value expression) is MORE THAN 8 units from 0.

Now, how does something get to be MORE THAN 8 units from 0?? It's either more than 8 units to the RIGHT of 0, or more than 8 units to the LEFT of 0, right?

So if it's more than 8 units to the right, then that means that: {something}>8
And if it's more than 8 units to the left, then that means that: {something}<-8

So there are TWO POSSIBILITIES:

{something}<-8 OR {something}>8

So use that to re-write an equivalent compound inequality, NOT using absolute value:

2x + 4 < -8 OR 2x + 4 > 8

Now you have two simple linear inequalities, solve each one separately, and then the union of the solution sets is the solution set to your abs value inequality.

Answer 2

how would i graph tht

Answer 3

What did you get for the solution?