N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
n+1≥6
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.

Answer 1

To solve the inequality \( n + 1 \geq 6 \), we need to isolate \( n \).

1. Subtract 1 from both sides: \[ n + 1 - 1 \geq 6 - 1 \] \[ n \geq 5 \]

The solution to the inequality is \( n \geq 5 \).

Graphing the Solution:

1. Plot the endpoint: Mark the point \( 5 \) on the number line.
2. Select the type of endpoint: Since the inequality is "greater than or equal to" (\(\geq\)), we will use a closed dot on the point \( 5 \) to indicate that \( 5 \) is included in the solution.
3. Draw the ray: From the point \( 5 \), draw a ray that extends to the right, indicating all numbers greater than \( 5 \).

The graph of the inequality \( n \geq 5 \) looks like this:

<---|---|---|---|---|---|---|---|---|--->
    3   4   •   6   7   8
                 n

The closed dot on \( 5 \) indicates it is part of the solution, and the arrow extends to the right, indicating that there are infinitely many solutions greater than \( 5 \).