How do you solve |5x-4| +3 = 3|5x4|+3=3?

1 Answer
Apr 29, 2017

See the solution process below:

Explanation:

First, subtract color(red)(3)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)|5x4|+33=33

abs(5x - 4) + 0 = 0|5x4|+0=0

abs(5x - 4) = 0|5x4|=0

Normally an absolute value equality would produce two answers. However, because the absolute value function is equal to 00 there is only one solution.

We can equate the term within the absolute value to 00 and solve for xx:

5x - 4 = 05x4=0

5x - 4 + color(red)(4) = 0 + color(red)(4)5x4+4=0+4

5x - 0 = 45x0=4

5x = 45x=4

(5x)/color(red)(5) = 4/color(red)(5)5x5=45

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

x = 4/5