Prove that if a1≤b1 and a2≤b2, then a1+a2≤b1+b2.

Primary tabs

Lesson Parent: 
Rules of Inequalities
Problem: 

Prove that if a1≤b1 and a2≤b2, then a1+a2≤b1+b2.

Answer: 

It is true that if a1≤b1 and a2≤b2, then a1+a2≤b1+b2.

SAMPLE SOLUTION

All of our problems have fully worked out, logical solutions. We connect every solution to its underlying lesson so you can understand the concepts needed to solve any problem and reinforce your learning by practicing with similar problems. All of the formulas are available to our subscribers, but here is a sample of the problem solution you will see when you log in:



Solution: 

This problem assumes that <Sign in to see all the formulas> and <Sign in to see all the formulas>. Let's add b2 to the first inequality to get

<Sign in to see all the formulas>


and add a1 to the second inequality to get

<Sign in to see all the formulas>


Therefore,

<Sign in to see all the formulas>


so we are guaranteed that

<Sign in to see all the formulas>

The proof is now complete.