Q67. - Algebra 2

Question

Solve each equation. Check the solution.

 

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

Step-by-Step Solution

Answer

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

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:

 

$\left|x\right|=7$

 

Case 1:

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

 

Or Case 2:

 

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

Step 3 - 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.

Step 4 - State the conclusion.

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