# Need help solving an inequality.

• Checkfate
I figured it outIn summary, after analyzing the function f(x) = 2 + x^(-3/2), it is clear that the domain is [0,inf) and the function is always greater than 0. This means that the solution to the inequality 2+x^(-3/2)>0 is x>(-2)^(-2/3). The mistake made by the poster was not taking into account the domain of the function.
Checkfate
I figured out the answer to the question I originally posted in this thread, but, I have another.

I am trying to solve $$2+x^{\frac{-3}{2}}>0$$

I end up with $$x>(-2)^{\frac{-2}{3}}$$ by just putting the 2 on the other side and solving. This is not the right answer though... what am I doing wrong? Thanks

Thats a 2+x^(-3/2) btw. (for the top tex) and a (-2)^(-2/3) for the bottom tex.

Last edited:
Try to look at the inequality f(x) > 0, where f(x) = 2 + x^(-3/2). Analyze the function.

Okay, I guess it makes more sense to do it that way :).

Since there is a x under a square root sign, the domain is [0,inf) and since the squareroot is always positive, the function is always > 0 :). Thanks,

## 1. What is an inequality?

An inequality is a mathematical statement that compares two values and shows their relationship. It can be expressed using symbols such as <, >, ≤, or ≥.

## 2. How do I solve an inequality?

To solve an inequality, you need to isolate the variable on one side of the inequality symbol and leave the constant on the other side. Then, you can use inverse operations to simplify and solve for the variable.

## 3. What are the different types of inequalities?

There are three main types of inequalities: linear inequalities, quadratic inequalities, and rational inequalities. Each type has its own specific rules and methods for solving.

## 4. Can I use the same rules for solving equations to solve inequalities?

No, the rules for solving inequalities are slightly different from those for solving equations. For example, when multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality symbol must be flipped.

## 5. How do I know if my solution to an inequality is correct?

To check if your solution is correct, you can substitute the value you found for the variable into the original inequality and see if it satisfies the inequality. If it does, then your solution is correct.

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