Q23. - Algebra 1

Question

Solve each equation. Then graph the solution set.

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

Step-by-Step Solution

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-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.