Question

solve the inequality and graph the solution.
45 < 15f
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.

Explanation:

Step1: Isolate the variable \( f \)

Divide both sides of the inequality \( 45 < 15f \) by \( 15 \).
$$\frac{45}{15}<\frac{15f}{15}$$

Step2: Simplify

Simplify the left - hand side \( \frac{45}{15}=3 \) and the right - hand side \( \frac{15f}{15}=f \). So the inequality becomes \( 3 < f \), which can be written as \( f>3 \).

To graph the solution:

• The inequality \( f > 3 \) has an open endpoint at \( f = 3 \) (because the inequality is strict, i.e., \( f\) is not equal to \( 3\)).
• The solution set is all real numbers greater than \( 3 \), so we draw a ray starting at \( 3 \) (with an open circle) and extending to the right.

Answer:

The solution of the inequality is \( f>3 \). On the number line, there is an open circle at \( 3 \) and a ray extending to the right.