Question

solve the inequality and graph the solution.
g - 11 ≥ - 19
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 \( 11 \) to both sides of the inequality \( g - 11\geq - 19 \).
Using the addition property of inequalities \( a\geq b\Rightarrow a + c\geq b + c\), we have \(g-11 + 11\geq-19 + 11\).
Simplifying gives \(g\geq-8\).

Step2: Graph the solution

For the inequality \(g\geq - 8\), on the number - line:

• The endpoint is at \(g=-8\). Since the inequality is \(\geq\) (greater than or equal to), the endpoint is a closed circle (to include \(-8\) in the solution set).
• The solution includes all values greater than \(-8\), so we draw a ray starting at \(-8\) and extending to the right.

Answer:

The solution of the inequality \(g - 11\geq - 19\) is \(g\geq - 8\). On the number - line, there is a closed circle at \(-8\) and a ray extending to the right.