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

1 Answer
Apr 29, 2017

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