Prove that if $a=bc$, $b\gt 0$ and $c\gt 1$, then $a\gt b$.

Primary tabs

Lesson Parent: 
Rules of Inequalities
Problem: 

Prove that if $a=bc$, $b\gt 0$ and $c\gt 1$, then $a\gt b$.

Answer: 

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

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: 

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>.