Solve |2x - 2| < 8 {x|-3 < x < 5}
{x|x < -3 or x > 5}
{x|-5 < x < 3}

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2x-2|

For the Negative case we'll use -(2x-2)

For the Positive case we'll use (2x-2)

-(2x-2) < 8

Multiply

-2x+2 < 8

Rearrange and Add up

-2x < 6

Divide both sides by 2

-x < 3

Multiply both sides by (-1)

Remember to flip the inequality sign

x > -3

Which is the solution for the Negative Case

(2x-2) < 8

Rearrange and Add up

2x < 10

Divide both sides by 2

x < 5

Which is the solution for the Positive Case

One solution was found :

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