Question

Solve the absolute value equation. |4x-1|=1

Answer 1

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 $x=0\quad \mathrm{or}\quad \:x=\frac{1}{2}$.

Answer 2

.5 because first you add 1 on each side, that gets rid of the 1 on the left. then divide by 4