Question

Question #60c7e

Answer 1

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

Explanation:

Isolate the `color(blue)"absolute value function"`

divide both sides of the equation by - 3

`(cancel(-3)|2x+6|)/cancel(-3)=(-12)/(-3)`

`rArr|2x+6|=4`

The absolute value can have a `color(blue)"positive or negative"` solution.

`rArr"solve "2x+6=color(red)(+-)4`

`• 2x+6=color(red)(+4)`

subtract 6 from both sides.

`2xcancel(+6)cancel(-6)=4-6`

`rArr2x=-2`

divide both sides by 2

`(cancel(2) x)/cancel(2)=(-2)/2`

`rArrx=-1tocolor(red)((1))`

`• 2x+6=-4`

`rArr2x=-10`

`rArrx=(-10)/2=-5tocolor(red)((2))`

`color(blue)"As a check"`

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

`• -3|-2+6|=-3|4|=-3xx4=-12`

`• -3|-10+6|=-3|-4|=-3xx4=-12`

`rArrx=-1" or "x=-5" are the solutions"`