Question

|x-5| = 4x + 1
Solve

Answer 1

Answer: 4/5

Explanation:

Note that:

`|x-5|=\begin{cases} x-5, x \geq 5 \\ 5-x, x < 5 \end{cases}`

Case 1:
`x \geq 5`

`x-5=4x+1\\\\-5=3x+1\\\\-4=3x\\\\x=-4/3`

However, this does not fall within the required interval, so we disregard this solution.

Case 2:
`x < 5`

`5-x=4x+1\\\\5=5x+1\\\\5x=4\\\\x=(4)/(5)`

This solution falls within the required interval, so we include it in the solution set.