Prove that if a1≤b1≤c1 and a2≤b2≤c2, then a1+a2≤b1+b2≤c1+c2.

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Lesson Parent: 
Rules of Inequalities
Problem: 

Prove that if a1≤b1≤c1 and a2≤b2≤c2, then a1+a2≤b1+b2≤c1+c2.

Answer: 

It is true that if a1≤b1≤c1 and a2≤b2≤c2, then a1+a2≤b1+b2≤c1+c2.

SAMPLE SOLUTION

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Solution: 

Let's break it into parts. First, we know that <Sign in to see all the formulas> and <Sign in to see all the formulas>. From this problem we know that

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Second, we know that <Sign in to see all the formulas> and <Sign in to see all the formulas>. From the same problem as above we know that

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The proof is now complete. We know that

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