Chapter 15.1, Problem 14PSC

To determine

To Prove: The given statement.

Explanation of Solution

Given:

  $\begin{array}{l}a,b\&c\text{ Real Numbers}\\ a>b\\ c-a<c-b\end{array}$

Formula Used:

  $a\left(c+d\right)=ac+ad$

Calculation:

  $\begin{array}{l}a,b\&c\text{ Real Numbers}\\ a>b\\ c-a<c-b\\ \therefore a-c>b-c\\ \text{On multiplying }-1\text{ both sides one will get}\\ \text{⇒}-1\left(a-c\right)>-1\left(b-c\right)\\ \text{⇒}c-a<c-b\end{array}$