Q38. - Algebra 1

Question

Solve each equation. Then graph the solution set.

$\left|-4d+6\right|=12$

Step-by-Step Solution

Answer

The equation $\left|-4d+6\right|=12$ has solution set as $d=-1.5$ and $d=4.5$ 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 − 4 d + 6 = 12 .

Simplify the expression for d.

$\begin{array}{c}-4d+6-6=12-6\\ -4d=6\\ \frac{-4d}{\left(-4\right)}=\frac{6}{\left(-4\right)}\\ d=-1.5\end{array}$

Step-3. Formulate case 2 when − 4 d + 6 = − 12 .

Simplify the expression for d.

$\begin{array}{c}-4d+6-6=-12-6\\ -4d=-18\\ -\frac{4d}{4}=\frac{-18}{4}\\ -d\times \left(-1\right)=-\text{4.5}\times \left(-1\right)\\ d=\text{4.5}\end{array}$

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

From case 1 and case 2, $d=-1.5,4.5$. Plot these values on the number line.