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#
