Question

Which inequality is equivalent to IX-4|<9

I need help this is on edge unity

Answer 1

`-5<x<13`

Explanation:

Inequalities and Absolute Value

The absolute value of any real number is defined as

`|x|=\left\{\begin{matrix}+x\ if\ x\ \geq 0\\ -x\ if\ x < 0\end{matrix}\right.`

If we know

`|f(x)|<a,\ for\ a>0`

Then these conditions must be met:

`f(x)<a,\ and\ f(x)>-a`

We have the inequality

`|x-4|<9`

It must be true that

`x-4<9`

Or

`x<13`

`x-4>-9`

Or

`x>-5`

Joining both conditions

`-5<x<13`

That is the solution of the original inequality