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

Question

asked Oct 9, 2020 63.2k views

2 Answers

Karmacon · Answer 1 · 2020-10-13T20:09:36+0000

Answer:

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

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