Question

Write the absolute value equation representing all numbers $\mathrm{x}$ whose distance from $4$ is $8$ units?

Answer 1

Step-1: Find the absolute value equation:

$\mathrm{x}$ is the set of numbers.

It is given that the distance of $\mathrm{x}$ from $4$ is $8$ units.

The distance of $\mathrm{x}$ from $4$ can be positive or negative.

Representing the distance between $\mathrm{x}$ and $4$ as follows:

$|\mathrm{x}-4|=8$

Step-2: Solve for $\mathrm{x}$:

Consider the distance $\mathrm{x}$ as positive

$$\begin{gathered} +(\mathrm{x}-4)=8 \\ \Rightarrow \mathrm{x}=8+4 \\ \Rightarrow \mathrm{x}=12 \end{gathered}$$

Consider the distance $\mathrm{x}$ as negative

$$\begin{gathered} -(\mathrm{x}-4)=8 \\ \Rightarrow -\mathrm{x}=8-4 \\ \Rightarrow -\mathrm{x}=4 \\ \Rightarrow \mathrm{x}=-4 \end{gathered}$$

Hence, the set of numbers $\mathrm{x}\in \{12,-4\}$ and the absolute value equation representing all numbers $\mathrm{x}$ is $\mathbf{|}\mathbf{x}\mathbf{-}\mathbf{4}\mathbf{|}\mathbf{=}\mathbf{8}\mathbf{}$.