Finding conditions for which an inequality holds

In summary, an inequality is a mathematical statement that compares two quantities. To find conditions for which an inequality holds, one must analyze the given inequality and determine what values make the statement true. This can be done by solving the inequality algebraically or graphically. Finding conditions for which an inequality holds is a broader concept than solving an inequality, as it involves determining a range of values that satisfy the statement. An inequality can have multiple solutions, meaning there can be more than one set of values that satisfy the statement. It is important to find conditions for which an inequality holds because it helps us understand the behavior of a mathematical expression or equation and make informed decisions in real-world applications.
  • #1
kalish1
99
0
Hello,
I do not know if this is the right place to post this question, but I believe it falls under algebra. Please redirect me if appropriate.

Question:

How can I show that $$P-QR^3<\frac{R^4}{C}$$ for $$C,P,Q,R > 0?$$

Thanks.
 
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  • #2
That statement is not true in general.
Consider $P=1000$, $Q=2$, $R=3$, $C=10000$, the inequality would be false.
 

FAQ: Finding conditions for which an inequality holds

What is an inequality?

An inequality is a mathematical statement that compares two quantities, expressing that one quantity is greater than, less than, or not equal to the other. It is represented by symbols such as <, >, ≤, ≥, or ≠.

How do you find conditions for which an inequality holds?

To find conditions for which an inequality holds, you need to analyze the given inequality and determine what values make the statement true. This can be done by solving the inequality algebraically or graphically, depending on the complexity of the inequality.

What is the difference between finding conditions for which an inequality holds and solving an inequality?

Finding conditions for which an inequality holds is a broader concept that involves determining a range of values for which the inequality statement is true. Solving an inequality, on the other hand, refers to finding specific values that satisfy the inequality.

Can an inequality have multiple solutions?

Yes, an inequality can have multiple solutions. This means there can be more than one set of values that satisfy the inequality statement. For example, in the inequality 2x + 5 < 15, x can take on any value less than 5 but greater than or equal to 0, resulting in multiple solutions.

Why is it important to find conditions for which an inequality holds?

Finding conditions for which an inequality holds is important because it helps us understand the behavior of a mathematical expression or equation. It also allows us to make informed decisions and draw conclusions based on the given inequality, which is crucial in many real-world applications such as economics, engineering, and science.

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