Question

solve the inequality and graph the solution.
-4f - 7 ≥ 5
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.

Explanation:

Step1: Add 7 to both sides

$$\begin{align*} -4f-7 + 7&\geq5 + 7\\ -4f&\geq12 \end{align*}$$

Step2: Divide both sides by -4 and reverse the inequality sign

$$\begin{align*} \frac{-4f}{-4}&\leq\frac{12}{-4}\\ f&\leq - 3 \end{align*}$$

To graph the solution: Plot a closed endpoint at -3 (since the inequality is $\leq$) and draw an arrow to the left.

Answer:

The solution of the inequality is \(f\leq - 3\). On the number - line, there is a closed circle at -3 and the ray extends to the left.