How do you simplify | 4-2x| > 2

Question

I need to know this for algebra, I know how to graph I just don't know how to simplify it.

Answer 1

An inequality containing an absolute value must be solved twice.

Once assuming the argument is positive, and once assuming the argument is negative

 

I.

Assume 4 - 2x is positive

 

|4 - 2x| > 2

4 - 2x > 2       subtract 4 from both sides

-2x > -2          divide both sides by -2 (order changes!)

x < 1

 

II.

Assume 4 - 2x is negative

|4 - 2x| > 2

-(4 - 2x) > 2     distribute

-4 + 2x > 2       add 4 to both sides

2x > 6             divide both sides by 2

x > 3