# Tough inequality

#### thereddevils

1. The problem statement, all variables and given/known data

For what values of the variable x does the following inequality hold:

$$\frac{4x^2}{(1-\sqrt{1+2x})^2}<2x+9$$

2. Relevant equations

3. The attempt at a solution

Maybe some hints for me to begin.

#### Mentallic

Homework Helper
The denominator is all squared so it must be positive (can't be zero). Therefore you can multiply through without worrying about changing the inequality sign and after that, expand, and leave the surd alone on one side, square the equation and you will get now have a polynomial of degree 4.

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