How do you solve #abs(-4+5x)=16#?

1 Answer
Apr 19, 2018

Answer:

#x=-12/5,4#

Explanation:

Solve:

#abs(-4+5x)=16#

Since #absa=+a and -a#, the equation can be broken into positive and a negative equations.

#-4+5x=16#

and

#-(-4+5x)=16#

Positive Equation

#-4+5x=16#

Add #4# to both sides.

#-color(red)cancel(color(black)(4))+color(red)cancel(color(black)(4))+5x=16+4#

Simplify.

#5x=20#

Divide both sides by #5#.

#(color(red)cancel(color(black)(5))x)/color(red)cancel(color(black)(5))=20/5#

Simplify.

#x=4#

Negative Equation

#-(-4+5x)=16#

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

#4-5x=16#

Subtract #4# from both sides.

#color(red)cancel(color(black)(4))-color(red)cancel(color(black)(4))-5x=16-4#

Simplify.

#-5x=12#

Divide both sides by #-5#.

#(color(red)cancel(color(black)(-5))x)/(color(red)cancel(color(black)(-5))x)=12/(-5)#

#x=-12/5#

Collect all solutions.

#x=-12/5,4#