Question

1. solve the inequality and graph the solution.

2n - 9 ≥ -1
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.
-5 -4 -3 2 -1 0 1 2 3 4 5

Explanation:

Step1: Add 9 to both sides

To isolate the term with \( n \), we add 9 to both sides of the inequality \( 2n - 9 \geq -1 \). This gives us \( 2n - 9 + 9 \geq -1 + 9 \), which simplifies to \( 2n \geq 8 \).

Step2: Divide by 2

Next, we divide both sides of the inequality \( 2n \geq 8 \) by 2 to solve for \( n \). So, \( \frac{2n}{2} \geq \frac{8}{2} \), which simplifies to \( n \geq 4 \).

To graph the solution:

• Plot a closed dot at \( n = 4 \) (since the inequality is "greater than or equal to", the endpoint is included).
• Draw an arrow to the right of 4 to indicate all numbers greater than or equal to 4.

Answer:

The solution to the inequality \( 2n - 9 \geq -1 \) is \( n \geq 4 \). The graph has a closed dot at 4 and an arrow pointing to the right.