Solve the inequality and graph the solution.

Question

2>
t
3
Plot the endpoints. Select an endpoint to change it from closed to open. Select the middle of the segment, ray, or line to delete it.

Answer 1

To solve the inequality \(2 > \frac{t}{3}\), we can start by manipulating the inequality to isolate \(t\).

1. Multiply both sides of the inequality by 3 (since 3 is a positive number, the direction of the inequality does not change):

\[ 2 \cdot 3 > t \]

\[ 6 > t \]

This can be rewritten as:

\[ t < 6 \]

Graphing the Solution

• The solution indicates that \(t\) can take any value less than 6.
• On a number line:
  • Place an open circle at 6 to indicate that 6 is not included in the solution (since \(t\) must be less than 6 but not equal to 6).
  • Shade to the left of the open circle to represent all the values less than 6.

Steps to Graph:

1. Place an open circle at 6 (as it is not included).
2. Shade the line to the left of the open circle to represent the values of \(t\) that satisfy the inequality \(t < 6\).

Summary of the Solution

The solution to the inequality is \(t < 6\), and the graph should display an open circle at 6 with shading extending to the left.