Question

solve the inequality and graph the solution.
9 ≥ -6 + 5m
to draw a ray, plot an endpoint and select an arrow. select an endpoint to change it from closed to open. select the middle of the ray to delete it.

Explanation:

Step1: Simplify the inequality

$$9\geq - 6 + 5m$$
Add \(6\) to both sides:
$$9 + 6\geq - 6+6 + 5m$$
$$15\geq5m$$

Step2: Solve for \(m\)

Divide both sides by \(5\):
$$\frac{15}{5}\geq\frac{5m}{5}$$
$$3\geq m$$
or \(m\leq3\)

To graph \(m\leq3\) on the number - line:

• The endpoint is at \(m = 3\). Since the inequality is \(\leq\) (closed - type inequality), the endpoint is a closed circle.
• The ray extends to the left (towards the smaller numbers) because \(m\) is less than or equal to \(3\).

Answer:

The solution of the inequality \(9\geq - 6 + 5m\) is \(m\leq3\). On the number - line, we plot a closed circle at \(3\) and draw a ray to the left.