Q37. - Algebra 1

Question

Solve each equation. Then graph the solution set.

$\left|-\frac{1}{2}b-2\right|=10$

Step-by-Step Solution

Answer

The equation $\left|-\frac{1}{2}b-2\right|=10$ has solution set as $b=-24$ and $b=16$ 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 − 1 2 b − 2 = 10 .

Simplify the expression for b.

$\begin{array}{c}-\frac{1}{2}b-2+2=10+2\\ -\frac{1}{\cancel{2}}b\times \left(-\cancel{2}\right)=12\times \left(-2\right)\\ b=-24\end{array}$

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

Simplify the expression for b.

$\begin{array}{c}-\frac{1}{2}b-2+2=-10+2\\ -\frac{1}{\cancel{2}}b\times \left(-\cancel{2}\right)=-8\times \left(-2\right)\\ b=16\end{array}$

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

From case 1 and case 2, $b=-24,16$. Plot these values on the number line.