Question

solve the inequality and graph the solution.
$4 \geq \frac{n}{2}$
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.
number line from 0 to 7 with ticks at 0,1,2,3,4,5,6,7

Explanation:

Step1: Multiply both sides by 2

To solve the inequality \(4 \geq \frac{n}{2}\), we multiply both sides by 2 to isolate \(n\). Multiplying both sides of an inequality by a positive number (2 in this case) does not change the direction of the inequality sign. So we have:
\(4\times2 \geq \frac{n}{2}\times2\)

Step2: Simplify both sides

Simplifying the left side: \(4\times2 = 8\)
Simplifying the right side: \(\frac{n}{2}\times2 = n\)
So the inequality becomes \(8 \geq n\), or equivalently \(n \leq 8\)

For graphing the solution on the number line:

• We have a closed circle at 8 (because the inequality is "less than or equal to", so 8 is included in the solution set).
• Then we draw an arrow to the left of 8 to represent all numbers less than or equal to 8.

Answer:

The solution to the inequality \(4 \geq \frac{n}{2}\) is \(n \leq 8\). To graph it, place a closed dot at 8 on the number line and draw an arrow pointing to the left.