Answer:
The solution is
.
Step-by-step explanation:
Given:
The inequality given is:
![|x|+4>7](https://tex.z-dn.net/?f=%7Cx%7C%2B4%3E7)
In order to simplify for 'x', we first isolate 'x' on one side.
Adding -4 on both sides, we get:
![|x|+4-4>7-4\\\\|x|>3](https://tex.z-dn.net/?f=%7Cx%7C%2B4-4%3E7-4%5C%5C%5C%5C%7Cx%7C%3E3)
Now,
is an absolute value function which is defined as:
![|x|=\left \{ {{-x}\ \ x](https://tex.z-dn.net/?f=%7Cx%7C%3D%5Cleft%20%5C%7B%20%7B%7B-x%7D%5C%20%5C%20x%3C0%20%5Catop%20%7Bx%5C%20%5C%20x%5Cgeq0%7D%7D%20%5Cright.)
Therefore, the given inequality can be rewritten as:
and ![x > 3](https://tex.z-dn.net/?f=x%20%3E%203)
Therefore, the solution is
.