Prove that if a=bc, b>0 and c>1, then a>b.

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Lesson Parent: 
Rules of Inequalities
Problem: 

Prove that if a=bc, b>0 and c>1, then a>b.

Answer: 

It is true that if a=bc, b>0 and c>1, then a>b.

SAMPLE SOLUTION

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Solution: 

We will use our rules of inequalities to prove this. Let's start with <Sign in to see all the formulas> and multiply both sides by b. Since b is positive then rule 2 tells us that <Sign in to see all the formulas>. But since a=bc, we have <Sign in to see all the formulas>. Therefore, <Sign in to see all the formulas>.