N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
4f<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 \( 4f < 8 \), we will follow these steps:

1. Isolate the variable: We will divide both sides of the inequality by 4.

   \[ \frac{4f}{4} < \frac{8}{4} \]

   This simplifies to:

   \[ f < 2 \]

2. Graph the solution: The solution \( f < 2 \) means that \( f \) can take any value less than 2.

   • To graph this inequality, plot an open circle at the point \( 2 \) (indicating that \( 2 \) is not included in the solution).
   • Draw a ray that extends to the left from the point \( 2 \) to indicate that all values less than \( 2 \) are included in the solution.

Here’s how you can visualize the graph:

• Open circle at 2: \( \bigodot \)
• Arrow pointing left:

<----(2

This means \( f < 2 \) is represented visually by an open circle at \( 2 \) with a line extending indefinitely to the left, indicating all numbers less than \( 2 \).