Question

solve the inequality and graph the solution.
f - 2 > 2
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 \( f \)

Add \( 2 \) to both sides of the inequality \( f - 2>2 \).
Using the addition property of inequalities (\( a>b\Rightarrow a + c>b + c\)), we get \( f-2 + 2>2+2 \).

Step2: Simplify the expressions

Simplify \( f-2 + 2\) to \( f \) and \( 2 + 2\) to \( 4\). So, \( f>4 \).

To graph \( f>4 \):

• The endpoint is \( 4 \). Since the inequality is \( > \) (not \( \geq \)), we use an open - circle at \( 4 \).
• The solution set includes all real numbers greater than \( 4 \), so we draw a ray starting at the open - circle at \( 4 \) and extending to the right.

Answer:

The solution of the inequality \( f - 2>2 \) is \( f>4 \). On the number - line, we have an open - circle at \( 4 \) and a ray extending to the right.