Q70. - Algebra 2

Question

Solve each equation. Check the solution.

 

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

Step-by-Step Solution

Answer

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

Step 1 - 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.

Step 2 - 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 $11$

Step 3 - 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.

Step 4 - State the conclusion.

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