right.azizlwl said:Homework Statement
Prove: If a>b and c>d, then a+c>b+d
Hint: (a-b)+(c-d)=(a+c)-(b+d)>0
Homework Equations
The Attempt at a Solution
How to use the hint to prove the inequality?
My method, not sure it's right.
Given c>d, c-d>0
Why not continue with the same line of thinking as above?azizlwl said:Given a>b => a+(c-d)>b
azizlwl said:Thus a+c>b+d
Proving an inequality means showing that the statement is true for all possible values of the variables involved. It involves using mathematical reasoning and logic to demonstrate that one side of the inequality is always greater than or less than the other side.
Proving inequalities is important because it allows us to compare and contrast different quantities and make conclusions about their relationships. This is especially useful in fields such as economics, physics, and statistics.
Some common techniques used to prove inequalities include mathematical induction, the method of contradiction, and the use of algebraic and geometric manipulations. Other methods such as the Cauchy-Schwarz inequality and the AM-GM inequality are also commonly used.
To determine if an inequality is true or false, you can use various methods such as plugging in values for the variables, graphing the inequality, or using mathematical proofs. In some cases, you may also need to use numerical or computational methods to verify the inequality.
Proving inequalities has many real-world applications, such as in optimizing production processes, analyzing financial investments, and determining the stability of physical systems. It is also commonly used in fields such as engineering, economics, and computer science.