Question

solve the inequality and graph the solution.
g - 5 ≤ 1
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 \( g \)

Add \( 5 \) to both sides of the inequality \( g - 5\leq1 \).
$$g-5 + 5\leq1 + 5$$

Step2: Simplify

Simplify the left - hand side \( g-5 + 5=g \) and the right - hand side \( 1 + 5 = 6 \). So, \( g\leq6 \).

To graph \( g\leq6 \):

• The endpoint is at \( g = 6 \). Since the inequality is \( \leq \) (less than or equal to), the endpoint is closed.
• The graph is a ray starting at \( 6 \) and extending to the left (towards smaller values of \( g \)).

Answer:

The solution of the inequality is \( g\leq6 \). On the number - line, there is a closed circle at \( 6 \) and a ray extending to the left.