Question

Solve each equation. Check the solution.

70. $\left|2\text{x}-36\right|=14$

Short answer

The value of $\text{x}$ is$\mathbf{25}$ and $\mathbf{11}$.

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:

$\left|2x-36\right|=14$

Case 1:

$\begin{array}{c}a=b\\ 2x-36=14\\ 2x-36+36=14+36\\ 2x=50\\ x=25\end{array}$

Or Case 2:

$\begin{array}{c}a=-b\\ 2x-36=-14\\ 2x-36+36=-14+36\\ 2x=22\\ x=11\end{array}$

The solution is $25$ and $11$

- Check the solution.

For case 1: $x=25$.

Check:

$\begin{array}{r}\left|2x-36\right|=14\\ \left|\left(2\times 25\right)-36\right|=14\\ \left|50-36\right|=14\\ \left|14\right|=14\\ 14=14\end{array}$

Thus, it is correct.

For case 2: $x=11$.

Check:

$\begin{array}{r}\left|2x-36\right|=14\\ \left|\left(2\times 11\right)-36\right|=14\\ \left|22-36\right|=14\\ \left|-14\right|=14\\ 14=14\end{array}$

Thus, it is also correct.

- State the conclusion.

Therefore, the solution set for x is $\left\{25,11\right\}$.