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.