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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