Question

Solve each equation. Then graph the solution set.

$\left|n-3\right|=5$

Short answer

The equation $\left|n-3\right|=5$has solution set as $n=8$and $n=-2$and the graph of the solution set is:

Step-by-step solution

Step-1. Define absolute value equation.

For any real numbers a and b, if$\left|a\right|=b$ and $b\ge 0$, then$a=b$ or $a=-b$.

Step-2. Formulate case 1 when n−3=5.

Simplify the expression for n.

$\begin{array}{c}n-3+3=5+3\\ n=8\end{array}$

Step-3. Formulate case 2 when n−3=−5.

Simplify the expression for n.

$\begin{array}{c}n-3+3=-5+3\\ n=-2\end{array}$

Step-4. Plot the graph of the solution set.

From case 1 and case 2, $n=8,-2$. Plot these values on the number line.