How do you solve #|5x-4| +3 = 3#?

1 Answer
Apr 29, 2017

Answer:

See the solution process below:

Explanation:

First, subtract #color(red)(3)# from each side of the equation to isolate the absolute value function while keeping the equation balanced:

#abs(5x - 4) + 3 - color(red)(3) = 3 - color(red)(3)#

#abs(5x - 4) + 0 = 0#

#abs(5x - 4) = 0#

Normally an absolute value equality would produce two answers. However, because the absolute value function is equal to #0# there is only one solution.

We can equate the term within the absolute value to #0# and solve for #x#:

#5x - 4 = 0#

#5x - 4 + color(red)(4) = 0 + color(red)(4)#

#5x - 0 = 4#

#5x = 4#

#(5x)/color(red)(5) = 4/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 4/5#

#x = 4/5#