Question

How do you solve `| 3 + 2x | >| 4 - x |`?

Answer 1

`x<-7 or x>1/3`

Explanation:

`abs(3+2x)>abs(4-x)`
Since both sides are positive
You can do the square at both sides to get rid of the abs sign
`because (abs(x))^2=(x)^2`

`(abs(3+2x))^2>(abs(4-x))^2`
`(3+2x)^2>(4-x)^2`
`9+12x+4x^2>16-8x+x^2`
`3x^2+20x-7>0`
`(3x-1)(x+7)>0`

`color(white)(....)`+`color(white)(..............)` `-` `color(white)(..................)` `+`
<--------`@` `color(white)(......................)` `@`-------------->
----------/--------------------------/-----------------
`color(white)(.....)` `-7` `color(white)(.......................)` `1/3`

`therefore x<-7 or x>1/3`