Question

How do you solve `|-5x + -2| + 3 = 11`?

Answer 1

`x=-2" or " x=6/5`

Explanation:

Equations involving the `color(blue)"absolute value"` have 2 solutions.

Isolate the absolute value, noting that

`-5x+ -2=-5x-2`

subtract 3 from both sides.

`|-5x-2|cancel(+3)cancel(-3)=11-3`

`rArr|-5x-2|=8`

The 2 solutions are obtained by solving `-5x-2=color(red)(+-)8`

`color(blue)"Solution 1"`

`-5x-2=8`

add 2 to both sides.

`-5xcancel(-2)cancel(+2)=8+2`

`rArr-5x=10rArrx=10/(-5)=-2`

`color(blue)"Solution 2"`

`-5x-2=-8`

add 2 to both sides.

`-5x=-8+2`

`rArr-5x=-6rArrx=(-6)/(-5)=6/5`

`color(blue)"As a check"`

`"left side "=|(-5xx-2)-2|+3=|8|+3=8+3=11 ✔︎`

`"left side "=|(-cancel(5)^1xx6/cancel(5)^1)-2|+3`

`=|-6-2|+3=|-8|+3=8+3=11 ✔︎`