Question

The absolute value inequality equation |2x – 1| > 3 will have what type of solution set?

Answer 1

Given:

The inequality is:

$|2x-1|>3$

To find:

The solution set for the given inequality.

Solution:

We know that, if $|x|>a$, then $x<-a$ and $x>a$.

We have,

$|2x-1|>3$

It can be written as:

$2x-1<-3$ or $2x-1>3$

Case I:

$2x-1<-3$

$2x<-3+1$

$2x<-2$

$x<\dfrac{-2}{2}$

$x<-1$

Case II:

$2x-1>3$

$2x>3+1$

$2x>4$

$x>\dfrac{4}{2}$

$x>2$

The required solution for the given inequality is $x<-1$ or $x>2$. The solution set in the interval notation is $(-\infty,-1)\cup (2,\infty)$.

Therefore, the required solution set is $(-\infty,-1)\cup (2,\infty)$.