Chapter 2.2, Problem 1E

To determine

To find: The reason for two inequalities are equivalent.

Answer to Problem 1E

Two inequalities are equivalent as by solving the second inequality, the same inequality we will get $x\le 6$ .

Explanation of Solution

Given information: Two inequalities given $x\le 6$ and $x-5\le 6-5$ .

Calculation:

Given two inequalities are $x\le 6$ and $x-5\le 6-5$

By solving the inequality,

  $\begin{array}{l}x-5\le 6-5\\ \Rightarrow x-5\le 1\\ \Rightarrow x\le 1+5\\ \Rightarrow x\le 6\end{array}$

So, the two inequalities are same as by solving the second inequality we can see it is as same as $x\le 6$ .