What is the solution set for $abs(2x + 4)< 8$ ?

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Answer 1 · 2018-05-02T15:08:04

$-6 < x < 2$ or $x in (-6,2)$

As $|2x+4|<8$ , then

either $2x+4<8$

i.e. $2x<8-4$

or $2x<4$ i.e, $x<2$

or $-(2x+4)<8$

i.e. $2x+4> -8$

or $2x> -8-4$

or $2x> -12$

or $x> -6$

Hence, $-6 < x < 2$ or $x in (-6,2)$

What is the solution set for abs(2x + 4)< 8abs(2x + 4)< 8?