How do you solve #12(16) = abs(19x-92)#?

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Answer 1 · 2018-05-27T22:28:18

#x=-100/19,284/19#

Solve:

#12(16)=abs(19x-92)#

Simplify #12(16)# to #192#

#192=abs(19x-92)#

Switch sides.

#abs(19x-92)=192#

Since #absa=a# and #abs(-a)=a#, we need to break down the equation into positive and negative equations.

#19x-92=192# and #-(19x-92)=192#

Positive equation

#19x-92=192#

Add #92# to both sides.

#19x=192+92#

#19x=284#

Divide both sides by #19#.

#x=284/19#

Negative equation

#-(19x-92)=192#

Distribute the #-1# on the left-hand side.

#-19x+92=192#

Subtract #92# from both sides.

#-19x=192-92#

#-19x=100#

Divide both sides by #-19#.

#x=-100/19#

Solutions for #x#.

#x=-100/19,284/19#