Question

Solve each equation. Then graph the solution set.

$\left|8w+5\right|=21$

Short answer

The equation $\left|8w+5\right|=21$has solution set as $w=-3.25$and $w=2$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 8w+5=21.

Simplify the expression for w.

$$\begin{gathered} 8w+5-5=21-5 \\ 8w=16 \\ \frac{8w}{8}=\frac{16}{8} \\ w=2 \end{gathered}$$

Step-3. Formulate case 2 when 8w+5=−21.

Simplify the expression for w.

$$\begin{gathered} 8w+5-5=-21-5 \\ 8w=-26 \\ \frac{8w}{8}=\frac{-26}{8} \\ w=-3.25 \end{gathered}$$

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

From case 1 and case 2, $w=-3.25,2$. Plot these values on the number line.