Q39. - Algebra 1

Question

Solve each equation. Then graph the solution set.

$\left|5f-3\right|=12$

Step-by-Step Solution

Answer

The equation $\left|5f-3\right|=12$ has solution set as $f=3$ and $f=-1.8$ 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 5 f − 3 = 12 .

Simplify the expression for f.

$\begin{array}{c}5f-3+3=12+3\\ 5f=15\\ \frac{5f}{5}=\frac{15}{5}\\ f=3\end{array}$

Step-3 – Formulate case 2 when 5 f − 3 = − 12 .

Simplify the expression for f.

$\begin{array}{c}5f-3+3=-12+3\\ 5f=-9\\ \frac{5f}{5}=\frac{-9}{5}\\ f=-\text{1.8}\end{array}$

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

From case 1 and case 2, $f=3,-1.8$. Plot these values on the number line.