Answer:
[tex]-5<x<13[/tex]
Step-by-step explanation:
Inequalities and Absolute Value
The absolute value of any real number is defined as
[tex]|x|=\left\{\begin{matrix}+x\ if\ x\ \geq 0\\ -x\ if\ x < 0\end{matrix}\right.[/tex]
If we know
[tex]|f(x)|<a,\ for\ a>0[/tex]
Then these conditions must be met:
[tex]f(x)<a,\ and\ f(x)>-a[/tex]
We have the inequality
[tex]|x-4|<9[/tex]
It must be true that
[tex]x-4<9[/tex]
Or
[tex]x<13[/tex]
[tex]x-4>-9[/tex]
Or
[tex]x>-5[/tex]
Joining both conditions
[tex]-5<x<13[/tex]
That is the solution of the original inequality
