Inequality proof problem

In summary, an inequality proof problem is a mathematical problem where one must prove that one side of an inequality statement is always greater than the other side. To solve these problems, one must understand the properties of inequalities and use algebraic techniques to manipulate the statement. Common mistakes to avoid include forgetting to flip the inequality sign and not considering all possible values. An example of an inequality proof problem is proving that x + y > 0 when x > 0 and y > 0. Understanding these problems can be useful in real-life situations such as budgeting and decision-making.
  • #1
annoymage
362
0

Homework Statement



l lxl - lyl l =< lx-yl

Homework Equations



n/a

The Attempt at a Solution



how do i proof this? give me a start please, should i use definition absolute values and consider all of the cases? or use triangle inequality(but i can't figure out how)
 
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  • #2


hey i get it, use x=(x-y)+y
 

1. What is an inequality proof problem?

An inequality proof problem is a mathematical problem that involves proving that one side of an inequality statement is always greater than the other side. This is typically done using algebraic or logical reasoning.

2. How do you approach solving an inequality proof problem?

To solve an inequality proof problem, you must first understand the properties of inequalities and the rules for manipulating them. Then, you can use algebraic techniques such as addition, subtraction, multiplication, and division to manipulate the inequality statement until you reach a logical conclusion.

3. Are there any common mistakes to avoid when solving an inequality proof problem?

Yes, some common mistakes to avoid include forgetting to flip the inequality sign when multiplying or dividing by a negative number, using incorrect mathematical operations, and not considering all possible values that could satisfy the inequality statement.

4. Can you provide an example of an inequality proof problem?

Sure, here is an example: Prove that for all real numbers x and y, if x > 0 and y > 0, then x + y > 0. To solve this problem, we can start by adding x and y to both sides of the inequality, which gives us x + y > x + y. Since x and y are both greater than 0, their sum must also be greater than 0, thus proving the inequality statement.

5. How can understanding inequality proof problems be useful in real-life?

Understanding inequality proof problems can be useful in many real-life situations, such as budgeting, investing, and decision-making. By being able to prove that one value is always greater than another, we can make informed choices and ensure fairness in various aspects of our lives.

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