N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
f+6≥8
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 \( f + 6 \geq 8 \), follow these steps:

Step 1: Solve the Inequality

1. Subtract 6 from both sides: \[ f + 6 - 6 \geq 8 - 6 \] Simplifying this gives: \[ f \geq 2 \]

Step 2: Graph the Solution

1. Plot the Endpoint: Since the inequality is \( f \geq 2 \), you will plot a closed circle (or dot) at \( 2 \) to indicate that \( 2 \) is included in the solution.
2. Draw the Ray: From the point \( 2 \), draw a ray extending to the right (to indicate all values greater than 2).

Final Representation

• The closed circle at \( 2 \) and the ray extending to the right indicates that all numbers greater than or equal to \( 2 \) are part of the solution set.

Summary

• The solution to the inequality \( f + 6 \geq 8 \) is \( f \geq 2 \).
• The graph would show a closed circle at \( 2 \) with a ray extending to the right.