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Chapter 6: Problem 9

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

Short Answer

Expert verified
The range (-2, 5] is graphed on a number line with an open circle above -2 (as -2 is not included), and a filled circle above 5 (as 5 is included). A line is drawn from -2 to 5 demonstrating all x-values in this range are in the set.

Step by step solution

01

Understand the Inequality

The inequality \(x \mid -2 < x \leq 5\) forms a range (-2, 5]. This indicates that the value of \(x\) is greater than -2 (not including -2, represented by '<') and less than or equal to 5 (including 5, represented by '\leq').
02

Prepare the Number Line

Draw a horizontal line, marking -2 and 5 along the line, along with a few other numbers for a scale reference.
03

Place the Symbols

As the value does not include -2, place an open circle above -2 on the number line. As it includes 5, place a filled circle above 5.
04

Mark the Inequality

Draw a line between -2 and 5, going through 5 while pointing right. This represents that all x's within this range are part of the set.

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