Chapter 4.3, Problem 46HP

To determine

To calculate:To find if the statement is always, never or sometimes true and explain the reasoning.

Answer to Problem 46HP

Real word problem is mentioned

Explanation of Solution

Given information:Statement is “If $a+x=100$ , then $x$ is less than $100$ ”

Calculation:

Statement is given as

“If $a+x=100$ , then $x$ is less than $100$ ”

The above statement is sometimes true.

Let us assume $a=-2$

Thus, on solving $a+x=100$ ,

$\begin{array}{l}-2+x=100\\ x=100+2\\ x=102\end{array}$

Here, $x$ is greater than 100.

Thus, the statement is false.

Letus assume $a=2$

Thus, on solving $a+x=100$ ,

$\begin{array}{l}2+x=100\\ x=100-2\\ x=98\end{array}$

Here, $x$ is less than 100.

Thus, the statement is true.