Mark M. answered • 08/15/16

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Mathematics Teacher - NCLB Highly Qualified

First, isolate the absolute value:

-8 + 2|4x + 6| > 20

2|4x + 6| > 28 add 8 to both sides

|4x + 6| > 14 divide both sides by 2

An absolute equation or inequality must be solved twice: once assuming the argument is positive and once assuming the argument is negative.

I. 4x + 6 is positive

4x + 6 > 14

4x > 8 subtract 6 from both sides

x > 2 divide both sides by 4

II. 4x + 6 is negative

-(4x + 6) > 14 the absolute value of negative is its opposite

-4x - 6 > 14 distribute

-4x > 20 add six to both sides

x < -5 divide both sides by -4 (note order of inequality changes)

x < -5 or 2 < x

Mark M.

08/15/16