Question

How do you solve `|-5x + -2| = 12`?

Answer 1

`x=-14/5` and `x=2`

Explanation:

We are given `abs(-5x+ -2)=12`. To solve this, we should first simplify the expression inside the absolute value bars, like this `-5x-2`. Okay... that's pretty much it. Now we move on to the next step.

Absolute value bars make whatever is within them positive. That means that we need to find two vaues for `x`: one positive and one negative.

So, instead of one equation, we have two. `abs(-5x-2)=12` becomes `-5x-2=12` and `-5x-2=-12`. Now we just solve for `x`.

`-5x-2=12` `color(white)(.......................)` `-5x-2=-12`
`color(white)(.....)+2color(white)()+2` `color(white)(.......................)` `color(white)(.........)+2color(white)(.......)+2`

`-5x=14` `color(white)(...............................)` `-5x=-10`
`color(white)(1)/-5color(white)(...)color(white)(1)/-5` `color(white)(...............................)` `color(white)(1)/-5color(white)(.......)color(white)(1)/-5`

`x=-14/5` `color(white)(...............................)` `x=2`

So, `x` is `-14/5` or `2` . If we want to, we can double check our answers by graphing the equation and see the `x`-intercepts.

graph{abs(-5x-2)-12=y}

We got it right!! Great job.