Question

Solve the absolute value equation |2x-1|=3

Answer 1

Answer:

The solution for the absolute value equation is  $x=-1\quad \mathrm{or}\quad \:x=2$.

Step-by-step explanation:

Consider the provided absolute value equation.  

$|2x-1|=3$

$\mathrm{If}\:|u|\:=\:a,\:a>0\:\mathrm{then}\:u\:=\:a\:\quad \mathrm{or}\quad \:u\:=\:-a$

By using the above rule.

$2x-1=-3\quad \mathrm{or}\quad \:2x-1=3$

$2x=-3+1\quad \mathrm{or}\quad \:2x=3+1$

$2x=-2\quad \mathrm{or}\quad \:2x=4$

$x=-1\quad \mathrm{or}\quad \:x=2$

Hence the combine solution is $x=-1\quad \mathrm{or}\quad \:x=2$

Answer 2

x=2

sorry for the bad handwriting btw.