Question #dd6bd

1 Answer
Sep 18, 2017

w < -2 and w > -4

Explanation:

2|w+3|-1<1
Let start by adding color(red)(1) to both sides
2|w+3|-1+color(red)(1)<1-color(red)1
2|w+3|<2
Divide both sides color(green)2
(2|w+3)/color(green)2 <2/color(green)2
|w+3|<1
We know w + 3 < 1 and w + 3 > -1
We have two conditions:
The first one is w + 3<1
The second one is w+3> -1

Let solve the first condition
w + 3 < 1
Subtract color(purple)3 from both sides
w + 3 - color(purple)3 < 1 - color(purple)3
w <-2

Let solve the second condition
w + 3 > -1
Subtract color(orange)3 from both sides
w+3-color(orange)3> -1 - color(orange)3
w > -4

Hence,

w<-2 and w> -4
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