Chapter 4, Problem 20CLR

To solve: the equation $\left|-x\right|=9$ over the set of real numbers.

To determine

  $x=-9,9$

Concept Used:

The absolute value of a number is the distance between the number and origin on the number line.

Explanation:

Consider the equation,

  $\left|-x\right|=9$

Since, the absolute value of a number is the distance between the number and origin on the number line. And it is known that any number and its corresponding positive number are at the same distance from the origin from the number line.

So, $\left|-x\right|=\left|x\right|$

So, $\left|-x\right|=9$ can be written as $\left|x\right|=9$

The only numbers whose distance from origin is 9 units are -9 and 9.

Thus, $x=-9,9$

Answer to Problem 20CLR

  $x=-9,9$

Explanation of Solution

Concept Used:

The absolute value of a number is the distance between the number and origin on the number line.

Consider the equation,

  $\left|-x\right|=9$

Since, the absolute value of a number is the distance between the number and origin on the number line. And it is known that any number and its corresponding positive number are at the same distance from the origin from the number line.

So, $\left|-x\right|=\left|x\right|$

So, $\left|-x\right|=9$ can be written as $\left|x\right|=9$

The only numbers whose distance from origin is 9 units are -9 and 9.

Thus, $x=-9,9$