Chapter 2.5, Problem 1E

To determine

To compare: the graph of $-6\le x\le -4$ with the graph of $x\le -6\text{ or }x\ge -4$ .

Answer to Problem 1E

First expression represents the points inside the interval $\left[-6,—4\right]$ while the second expression represents the points outside the interval, including the boundaries: $(-\infty ,-6]\cup [-4,\infty )$

Explanation of Solution

Given:

  $\begin{array}{l}-6\le x\le -4\\ x\le -6\text{ or }x\ge -4\end{array}$

Calculation:

The graph of $-6\le x\le -4$ represents the points which lie between $-6and-4$ , while the graph of $x\le -6\text{ or }x\ge -4$ represents the points which lie on the left of -6 and on the right of $-4$ .

So the first expression represents the points inside the interval $\left[-6,—4\right]$ while the second expression represents the points outside the interval, including the boundaries: $(-\infty ,-6]\cup [-4,\infty )$ .

Conclusion:

First expression represents the points inside the interval $\left[-6,—4\right]$ while the second expression represents the points outside the interval, including the boundaries: $(-\infty ,-6]\cup [-4,\infty )$