# 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 ____”.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

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 |x|<3_”.

### Explanation of Solution

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, |x|<3.

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 |x|<3_”.

(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 |x|>3_”.

### Explanation of Solution

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, |x|>3.

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 |x|>3_”.

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