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6th Edition

Stewart + 5 others

Publisher: Cengage Learning

ISBN: 9780840068071

Chapter 1.7, Problem 4E

(**a**)

To determine

**To fill:** The blank in the statement “The set of all points on the real line whose distance from zero is less than 3 can be described by the absolute value inequality ____”.

Expert Solution

The complete statement is “The set of all points on the real line whose distance from zero is less than 3 can be described by the absolute value inequality

**Definition used:**

The absolute value of a real number is defined as the distance of that number from zero (the origin) on a number line.

**Calculation:**

Since the distance of a number from zero on a number line is the absolute value of that number, the set of all points *x* on the real line whose distance from zero is less than 3 will be the set of all points on the number line, whose absolute value is less than 3.

That is,

Thus, the complete statement is “The set of all points on the real line whose distance from zero is less than 3 can be described by the absolute value inequality

(**b**)

To determine

**To fill:** The blank in the statement “The set of all points on the real line whose distance from zero is greater than 3 can be described by the absolute value inequality ____”.

Expert Solution

The complete statement is “The set of all points on the real line whose distance from zero is greater than 3 can be described by the absolute value inequality

Since the distance of a number from zero on a number line is the absolute value of that number, the set of all points *x* on the real line whose distance from zero is greater than 3 will be the set of all points on the number line, whose absolute value is greater than 3.

That is,

Thus, the complete statement is “The set of all points on the real line whose distance from zero is greater than 3 can be described by the absolute value inequality