Question

How do you solve for x: `−5|3x − 2| = −15`?

Answer 1

`x=-1/3" or "x=5/3`

Explanation:

`color(blue)"Isolate " |3x-5|" by dividing both sides by - 5"`

`cancel(-5)/cancel(-5)|3x-2|=(-15)/(-5)`

`rArr|3x-2|=3`

`"the expression inside the bars can be positive or negative"`

`"hence there are 2 possible solutions"`

`color(red)(+-)(3x-2)=3`

`color(blue)"First solution"`

`3x-2=3`

`"add 2 to both sides"`

`3xcancel(-2)cancel(+2)=3+2`

`rArr3x=5`

`"divide both sides by 3"`

`(cancel(3) x)/cancel(3)=5/3`

`rArrx=5/3`

`color(blue)"Second solution"`

`-(3x-2)=3`

`rArr-3x+2=3`

`"subtract 2 from both sides"`

`rArr-3x=1`

`"divide both sides by - 3"`

`rArrx=-1/3`