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Chapter 6: Problem 2

Graph each set of real numbers on a number line. \(\\{x \mid x>-2\\}\)

Short Answer

Expert verified
-2 is represented by an open circle on the number line, and all points to the right of -2 represent the solutions to the inequality.

Step by step solution

01

Identify the inequality

First, identify what the inequality in the given set notation tells us. In this case, \(x > -2\) means that x is greater than -2. Thus, the set of numbers includes all real numbers greater than -2.
02

Draw the number line

Next, draw a straight horizontal line. This represents the number line. It helps us visualize where the values of x are located.
03

Mark and label a point on the number line

Locate -2 on the number line. Usually, a smaller tick mark denotes each integer point. Mark the -2 point.
04

Represent the inequality on the number line

The inequality \(x > -2\) means x is greater than -2 but it does not include -2. Indicate this by drawing an open circle at -2. Then draw a line going to the right from the open circle at -2 to represent all numbers greater than -2.

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