Question

Solve each equation. Check the solution.

59. If $\left|\text{x}-3\right|=17$

Short answer

The value of $\text{x}$ is$\mathbf{20}$ and $-\mathbf{14}$.

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:

$\left|x-3\right|=17$

Case 1:

$\begin{array}{c}a=b\\ x-3=17\\ x-3+3=17+3\\ x=20\end{array}$

Or Case 2:

$\begin{array}{c}a=-b\\ x-3=-17\\ x-3+3=-17+3\\ x=-14\end{array}$

The solution is $20$and $-14$

- Check the solution.

For case 1: $x=20$.

Check:

$\begin{array}{r}\left|x-3\right|=17\\ \left|20-3\right|=17\\ \left|17\right|=17\\ 17=17\end{array}$

Thus, it is correct.

For case 2: $x=-14$.

Check:

$\begin{array}{r}\left|x-3\right|=17\\ \left|-14-3\right|=17\\ \left|-17\right|=17\\ 17=17\end{array}$

Thus, it is also correct.

- State the conclusion.

Therefore, the solution set for $x$ is $\left\{20,-14\right\}$.