Q64. - Algebra 2

Question

Solve each equation. Check your solution.

 

$\left|x\right|-5=8$

Step-by-Step Solution

Answer

The solutions of the equation are $x=-13$ and $x=13$.

Step-1 – Apply the concept of Absolute value

On real number line, the distance of a number from 0 is the absolute value. It is always nonnegative.

The absolute value of a function is expressed as, if x is a real number then absolute value of x is defined as.

$\left|x\right|=x$ when x is greater than or equal to 0 . In other words, the absolute value of x is x when x is either positive or zero.

$\left|x\right|=-x$ when x is less than 0 . In other words, the absolute value of x is opposite of x when x is negative.

Step-2 –Example of Absolute value

The absolute value of 5 is expressed as $\left|5\right|=5$ and of $-5$ is expressed as $\left|-5\right|=5$

Step-3 – Simplify the equation

Consider the provided equation.

$\left|x\right|-5=8$

Add 5 to both the sides.

$\begin{array}{c}\left|x\right|-5+5=8+5\\ \left|x\right|=13\end{array}$

Recall the concept of absolute value and apply it.

Case 1. $x=-13$

Case 2. $x=13$

Therefore, there are two possible solutions for the equation $\left|x\right|-5=8$ that are $x=-13$ and $x=13$.

Step-4 – Verify the solutions

Substitute the value $x=-13$ in the equation $\left|x\right|-5=8$.

$\begin{array}{c}\left|-13\right|-5=8\\ 13-5=8\\ 8=8\end{array}$

Since, this is true so the value $x=-13$ satisfy the equation $\left|x\right|-5=8$.

Substitute the value x=13 in the equation $\left|x\right|-5=8$.

$\begin{array}{c}\left|13\right|-5=8\\ 13-5=8\\ 8=8\end{array}$

Since, this is true so the value $x=13$ satisfy the equation $\left|x\right|-5=8$.

Thus, the solution set is $\left\{-13,13\right\}$.

Hence, the solutions of the equation are $x=-13$ and $x=13$.