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 \( g-11 + 11\geq-19 + 11\).

Step2: Simplify the expressions

Simplify the left - hand side: \( g-11 + 11=g\).
Simplify the right - hand side: \(-19 + 11=-8\). So, \( g\geq - 8\).

To graph \( g\geq - 8\):

• Place a closed circle at \( - 8\) (because the inequality is \(\geq\), which includes the endpoint).
• Draw a ray to the right of \( - 8\) (since \( g\) is greater than or equal to \( - 8\)).

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.