Question

Solve each equation. Check the solution.

$\left|\text{x}\right|=7$

Short answer

The value of $\text{x}$ is$\mathbf{7}$ and $-\mathbf{7}$.

Step-by-step solution

- State the definition of absolute value.

The distance of a number from 0 in the number line is called the absolute value and since distance cannot be negative so absolute value is always positive.

- Solve the inequality.

If x is a number, then absolute value of x is written as $\left|x\right|$.

Here, the inequality is:

$\left|x\right|=7$

Case 1:

$\begin{array}{c}a=b\\ x=7\end{array}$

Or Case 2:

$\begin{array}{c}a=-b\\ x=-7\end{array}$

- Check the solution.

For case 1: $x=7$.

Check:

$\begin{array}{c}\left|x\right|=7\\ \left|7\right|=7\\ 7=7\end{array}$

Thus, it is correct.

For case 2: $x=-7$.

Check:

$\begin{array}{c}\left|x\right|=7\\ \left|-7\right|=7\\ 7=7\end{array}$

Thus, it is also correct.

- State the conclusion.

Therefore, the solution set for x is $\left\{7,-7\right\}$.