Question 389529
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|-2x-4|<12

Remove the absolute value term.  This creates a \ on the right-hand side of the equation because |x|=\x.
-2x-4<\(12)

Set up the + portion of the \ solution.
-2x-4<12

Move all terms not containing x to the right-hand side of the inequality.
-2x<16

Divide each term in the inequality by -2.
x>-8

Set up the - portion of the \ solution.  When solving the - portion of an inequality, flip the direction of the inequality sign.
-2x-4>-(12)

Multiply -1 by the 12 inside the parentheses.
-2x-4>-12

Since -4 does not contain the variable to solve for, move it to the right-hand side of the inequality by adding 4 to both sides.
-2x>4-12

Subtract 12 from 4 to get -8.
-2x>-8

Divide each term in the inequality by -2.
-(2x)/(-2)<-(8)/(-2)

Simplify the left-hand side of the inequality by canceling the common factors.
x<-(8)/(-2)

Simplify the right-hand side of the inequality by simplifying each term.
x<4

The solution to the inequality includes both the positive and negative versions of the absolute value.
x>-8 and x<4

The solution is the set of values where x>-8 and x<4.
-8<x<4