Chapter 2.2, Problem 1E

To determine

To explain:

The similarity between two inequality equations $x\le 6$ and $x-5\le 6-5$ .

Answer to Problem 1E

On solving the second inequality equation $x-5\le 6-5$ , the result is same as first $x\le 6$ , so both are equivalent.

Explanation of Solution

Given information:

  $x\le 6$ and $x-5\le 6-5$ .

The two inequality equations are given as:

  $x\le 6$.......... (1)

  $x-5\le 6-5$......... (2)

Modify eq. (2) as:

  $x-5\le 6-5$

Add $5$ on both sides of equations:

  $\begin{array}{l}x-5\le 6-5\\ x-5+5\le 6-5+5\end{array}$

  $x\le 6$.......... (3)

From eq. (1) and (3), both are same.

Hence, the inequality shown by $x\le 6$ is equivalent to the inequality of $x-5\le 6-5$ .