Prove that if $a\gt 0$ and $b\gt 0$, then $a+b\gt a$ and $a+b\gt b$.

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Lesson Parent: 
Rules of Inequalities
Problem: 

Prove that if $a\gt 0$ and $b\gt 0$, then $a+b\gt a$ and $a+b\gt b$.

Answer: 

It is true that if $a\gt 0$ and $b\gt 0$, then $a+b\gt a$ and $a+b\gt b$.

SAMPLE SOLUTION

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Solution: 

This follows almost perfectly from our rules of inequalities. We can add a number to both sides of the inequality sign without changing it (unlike multiplying by a negative number). So given <Sign in to see all the formulas> we have

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Similary, given <Sign in to see all the formulas> we have

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