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