Question

1. solve the inequality and graph the solution. 12 ≥ 4r 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. 0 1 2 3 4 5 6 7

Explanation:

Step1: Divide both sides by 4

To solve the inequality \(12 \geq 4r\), we divide both sides by 4 (since 4 is positive, the inequality sign remains the same). So we have \(\frac{12}{4} \geq \frac{4r}{4}\).

Step2: Simplify both sides

Simplifying \(\frac{12}{4}\) gives 3, and \(\frac{4r}{4}\) simplifies to \(r\). So the inequality becomes \(3 \geq r\) or \(r \leq 3\).

For graphing: We plot a closed dot at 3 (because the inequality is "less than or equal to", so 3 is included in the solution) and draw a ray to the left (towards decreasing values of \(r\)) to represent all numbers less than or equal to 3.

Answer:

The solution to the inequality is \(r \leq 3\). For the graph, there is a closed endpoint at 3 on the number line, and the ray extends to the left from 3.