Question

How do you solve `abs(3x+2)<7`?

Answer 1

`-3 < x<5/3`

Explanation:

Inequalities of the type `|x|< a` always have solutions of the form

`-a < x< a`

`rArr-7 < 3x+2 < 7`

`color(blue)" Isolate " x " in the centre interval"`

`"subtract 2 from ALL three intervals"`

`-7-2 < 3xcancel(+2)cancel(-2)<7-2`

`rArr-9 < 3x < 5`

`"divide ALL three intervals by 3"`

`(-9)/3 < (cancel(3) x)/cancel(3) < 5/3`

`rArr-3 < x < 5/3" is the solution"`