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Chapter 6: Problem 6

Graph each set of real numbers on a number line. \(\\{x \mid x \geq-5\\}\)

Short Answer

Expert verified
To graph the set \(x \geq -5\) on a number line, a circle should be drawn around -5 indicating this value is included, and an arrow should be drawn to the right of -5, extending towards positive infinity. This indicates that all numbers greater than or equal to -5 are included in the set.

Step by step solution

01

Understand the inequality

The inequality \(x \geq -5\) means that \(x\) can be any number that is greater than or equal to -5. This includes -5 itself and all the numbers to the right of -5 on a number line.
02

Draw the number line

Draw a straight, horizontal line. This will represent our number line. Mark a point to represent the number -5 on this line. For inequalities that include the value in the set, like \(x \geq -5\), make this point solid to show that -5 is included in the set.
03

Represent the set on the number line

To represent the set \(x \geq -5\) on the number line, we need to show all the numbers greater than or equal to -5. Draw an arrow pointing to the right starting at -5. This indicates that the set includes all real numbers greater than -5, up to positive infinity.

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