N.5 Graph solutions to one-step inequalities

Question

TMX
Solve the inequality and graph the solution.
t+3>5
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 \( t + 3 > 5 \), we can isolate \( t \) by following these steps:

1. Subtract 3 from both sides: \[ t + 3 - 3 > 5 - 3 \] This simplifies to: \[ t > 2 \]

Now that we have the solution \( t > 2 \), we can graph this on a number line.

Steps to graph the solution \( t > 2 \):

1. Draw a number line.
2. Plot the point 2 on the number line.
3. Since 2 is not included in the solution, use an open circle at the point 2.
4. Draw a ray extending to the right from the open circle (indicating all numbers greater than 2).

The result is a graph showing all numbers greater than 2, represented visually with an open circle at 2 and a solid line extending to the right.

Summary of the Graph:

• Open circle at 2
• Arrow extending right (toward positive infinity)

This represents the solution set for the inequality \( t > 2 \).