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thereddevils
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Homework Statement
For what values of the variable x does the following inequality hold:
[tex]\frac{4x^2}{(1-\sqrt{1+2x})^2}<2x+9[/tex]
Homework Equations
The Attempt at a Solution
Maybe some hints for me to begin.
The inequality to solve is 4x^2/(1-√(1+2x))^2 < 2x+9.
The first step is to simplify the square root in the denominator by using the property √(a+b) = √a + √b.
The next step is to multiply both sides of the inequality by the denominator squared to eliminate it from the equation.
The final solution is x < -3. This can be found by solving for x in the resulting quadratic equation and then checking if the solution satisfies the original inequality.
The solution x < -3 means that any value of x less than -3 will make the inequality true. Therefore, the solution set for this inequality is all real numbers less than -3.