Question

The symbol $\left|x\right|$stands for the _______ of the number x.

If x is not 0, then the sign of $\left|x\right|$is always _______.

Short answer

The symbol $\left|x\right|$ stands for the absolute value of the number x. If x is not 0, then the sign of$\left|x\right|$ is alwayspositive.

Step-by-step solution

Step 1. State the concept.

The absolute value of a number x, denoted by $\left|x\right|$ is the distance of x from 0 on the real number line. Since distance is always positive,$\left|x\right|$ is always positive or 0, when $x=0$.

Step 2. List the given data.

The given incomplete statements are as follows:

The symbol$\left|x\right|$ stands for the _______ of the number x. If x is not 0, then the sign of$\left|x\right|$ is always _______.

Step 3. Complete the statement.

Applying the definition of the absolute value of a real number, the complete statements are:

The symbol $\left|x\right|$stands for the absolute value of the number x. If x is not 0, then the sign of$\left|x\right|$ is always positive.