Q26. - Algebra 1

Question

Solve each equation. Then graph the solution set.

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

Step-by-Step Solution

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-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 8 w + 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 8 w + 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.