Question

use the number line to represent the solution to \\( \frac{x}{2} \geq 4 \\). click on the appropriate ray to select it, then click on the location of the endpoint of the ray to place it on the number line.

Explanation:

Step1: Solve the inequality

We have the inequality $\frac{x}{2} \geq 4$. To solve for $x$, we multiply both sides of the inequality by 2:

$$\begin{align*} \frac{x}{2} \times 2 &\geq 4 \times 2\\ x &\geq 8 \end{align*}$$

Step2: Represent on the number line

On the number line, we need to show all numbers greater than or equal to 8. So we select the ray that starts at 8 (including 8, so we use a closed dot at 8) and extends to the right (since $x$ is greater than or equal to 8).

Answer:

To represent the solution $x \geq 8$ on the number line, place a closed dot at 8 and draw a ray extending to the right (towards 9, 10, etc.).