Solve Inequality: 4x^2/(1-√(1+2x))^2 < 2x+9

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In summary, the inequality to solve is 4x^2/(1-√(1+2x))^2 < 2x+9. The first step in solving this inequality 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, which 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
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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.
 
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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.
 

FAQ: Solve Inequality: 4x^2/(1-√(1+2x))^2 < 2x+9

What is the inequality to solve?

The inequality to solve is 4x^2/(1-√(1+2x))^2 < 2x+9.

What is the first step in solving this inequality?

The first step is to simplify the square root in the denominator by using the property √(a+b) = √a + √b.

What is the next step after simplifying the square root?

The next step is to multiply both sides of the inequality by the denominator squared to eliminate it from the equation.

What is the final solution to this inequality?

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.

What is the significance of the solution x < -3?

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.

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