Q25. - Algebra 1

Question

Solve each equation. Then graph the solution set.

$\left|4t-8\right|=20$

Step-by-Step Solution

Answer

The equation $\left|4t-8\right|=20$ has solution set as $t=7$ and $t=-3$ 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 t − 8 = 20 .

Simplify the expression for t.

$$\begin{gathered} 4t-8+8=20+8 \\ 4t=28 \\ \frac{ 4t}{4}=\frac{28}{4} \\ t=7 \end{gathered}$$

Step-3. Formulate case 2 when 4 t − 8 = − 20 .

Simplify the expression for t.

$$\begin{gathered} 4t-8+8=-20+8 \\ 4t=-12 \\ \frac{ 4t}{4}=\frac{-12}{4} \\ t=-3 \end{gathered}$$

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

From case 1 and case 2, $t=7,-3$. Plot these values on the number line.