Question

Solve each equation. Then graph the solution set.

$\left|f+10\right|=1$

Short answer

The equation $\left|f+10\right|=1$has solution set as $n=-9$and $n=-11$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 f+10=1.

Simplify the expression for f.

$\begin{array}{c}f+10-10=1-10\\ f=-9\end{array}$

Step-3. Formulate case 2 when f+10=−1.

Simplify the expression for f.

$\begin{array}{c}f+10-10=-1-10\\ f=-11\end{array}$

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

From case 1 and case 2, $f=-9,-11$. Plot these values on the number line.