Prove that if $a_1\leq b_1$ and $a_2\leq b_2$, then $a_1+a_2\leq b_1+b_2$.

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Lesson Parent: 
Rules of Inequalities
Problem: 

Prove that if $a_1\leq b_1$ and $a_2\leq b_2$, then $a_1+a_2\leq b_1+b_2$.

Answer: 

It is true that if $a_1\leq b_1$ and $a_2\leq b_2$, then $a_1+a_2\leq b_1+b_2$.

SAMPLE SOLUTION

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Solution: 

This problem assumes that <Sign in to see all the formulas> and <Sign in to see all the formulas>. Let's add $b_2$ to the first inequality to get

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and add $a_1$ to the second inequality to get

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Therefore,

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so we are guaranteed that

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The proof is now complete.