Answer:
The solution for the absolute value equation is \(x=0\quad \mathrm{or}\quad \:x=\frac{1}{2}\).
Step-by-step explanation:
Consider the provided expression.
\(|4x-1|=1\)
Apply the absolute rule:
\(\mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a\)
\(4x-1=-1\quad \mathrm{or}\quad \:4x-1=1\)
\(4x=-1+1\quad \mathrm{or}\quad \:4x=1+1\)
\(4x=0\quad \mathrm{or}\quad \:4x=2\)
\(x=0\quad \mathrm{or}\quad \:x=\frac{1}{2}\)
Hence, the solution for the absolute value equation is \(x=0\quad \mathrm{or}\quad \:x=\frac{1}{2}\).
