Question

Solve and graph each solution set .-25 < f(x) < 0 , where f (x) = - 3x -4

Answer 1

In order to solve and graph the solution set, let's write two inequalities from the given expression:

$\begin{cases}-3x-4>-25 \\ -3x-4<0\end{cases}$

Solving each one, we have:

$\begin{gathered} -3x-4>-25 \\ -3x>-25+4 \\ -3x>-21 \\ 3x<21 \\ x<7 \\ \\ -3x-4<0 \\ -3x<4 \\ 3x>-4 \\ x>-\frac{4}{3} \end{gathered}$

Now, graphing both solutions in the same number line, we have:

The solution set in interval notation is:

$(-\frac{4}{3},7)$