Question

graph the inequality on the number line.
$x \geq -3 \frac{1}{2}$

Explanation:

Step1: Identify the boundary value

The inequality is $x \geq -3\frac{1}{2}$, so the boundary point is $-3\frac{1}{2} = -\frac{7}{2} = -3.5$, which lies halfway between $-4$ and $-3$ on the number line.

Step2: Determine the boundary style

Since the inequality uses $\geq$ (greater than or equal to), the boundary point is included. We use a closed (filled) dot at $-3.5$.

Step3: Determine the direction of shading

The inequality $x \geq -3.5$ means all values greater than or equal to $-3.5$, so we shade the number line to the right of the closed dot at $-3.5$.

Answer:

1. Place a closed (filled) dot at the point halfway between $-4$ and $-3$ (representing $-3\frac{1}{2}$) on the number line.
2. Draw a solid arrow extending to the right from this dot, covering all values greater than $-3\frac{1}{2}$.