
Mark M. answered 08/15/16
Tutor
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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