Q68. - Algebra 2

Question

Solve each equation. Check the solution.

 

68. $\left|\text{x}+5\right|=18$

Step-by-Step Solution

Answer

The value of $\text{x}$ is $\mathbf{13}$ and $-\mathbf{23}$.

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:

 

$\left|x+5\right|=18$

 

Case 1: 

 

$\begin{array}{c}a=b\\ x+5=18\\ x+5-5=18-5\\ x=13\end{array}$

 

Or Case 2:

 

$\begin{array}{c}a=-b\\ x+5=-18\\ x+5-5=-18-5\\ x=-23\end{array}$

 

The solution is $13$ and $-23$

Step 3 - Check the solution.

For case 1: $x=13$.

 

Check:

 

$\begin{array}{r}\left|x+5\right|=18\\ \left|13+5\right|=18\\ \left|18\right|=18\\ 18=18\end{array}$

 

Thus, it is correct.

 

For case 2: $x=-23$.

 

Check:

 

$\begin{array}{r}\left|x+5\right|=18\\ \left|-23+5\right|=18\\ \left|-18\right|=18\\ 18=18\end{array}$

 

Thus, it is also correct.

Step 4 - State the conclusion.

Therefore, the solution set for x is $\left\{13,-23\right\}$.