Q32. - Algebra 1

Question

Solve each compound inequality. Then graph the solution set.

$-4<2t-6<8$

Step-by-Step Solution

Answer

The solution of the given compound inequality $-4<2t-6<8$ is $t\in \left(1,7\right)$.

The graph of the solution set which is $t\in \left(1,7\right)$ is:

Step 1. Solve the given compound inequality &#8722; 4 &#60; 2 t &#8722; 6 &#60; 8 .

The solution of the given compound inequality $-4<2t-6<8$ is:

$$\begin{gathered} -4<2t-6<8 \\ -4+6<2t-6+6<8+6 \\ 2<2t<14 \\ \frac{2}{2}<\frac{2t}{2}<\frac{14}{2} \\ 1<t<7 \end{gathered}$$

Therefore, the solution of the compound inequality $-4<2t-6<8$ is $t\in \left(1,7\right)$.

Step 2. Draw the graph of the solution set which is t &#8712; 1 , 7 .

The graph of the solution set which is $t\in \left(1,7\right)$ is: