Question

Question #dd6bd

Answer 1

`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`