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

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Answer 1 · 2018-05-02T15:08:04

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

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

either $2 x + 4 < 8$ $2x+4<8$

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

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

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

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

or $2 x > - 8 - 4$ $2x> -8-4$

or $2 x > - 12$ $2x> -12$

or $x > - 6$ $x> -6$

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

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