Question

solve the inequality and graph the solution.
\\(\frac{n}{2} + 4 \geq 5\\)
plot the endpoints. select an endpoint to change it from closed to open. select the middle of the segment, ray, or line to delete it.
(number line with ticks at -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5)

Explanation:

Step1: Subtract 4 from both sides

To isolate the term with \( n \), we subtract 4 from both sides of the inequality \( \frac{n}{2} + 4 \geq 5 \). This gives us \( \frac{n}{2} + 4 - 4 \geq 5 - 4 \), which simplifies to \( \frac{n}{2} \geq 1 \).

Step2: Multiply both sides by 2

To solve for \( n \), we multiply both sides of the inequality \( \frac{n}{2} \geq 1 \) by 2. This gives us \( \frac{n}{2} \times 2 \geq 1 \times 2 \), which simplifies to \( n \geq 2 \).

Answer:

The solution to the inequality is \( n \geq 2 \). To graph this, we plot a closed dot at \( n = 2 \) (since the inequality is "greater than or equal to") and draw a ray to the right of 2 on the number line.