Solve the inequality and graph the solution.

Question

t+2
–
1
≥1
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:

\[ \frac{t + 2}{1} \geq 1 \]

We first simplify this to:

\[ t + 2 \geq 1 \]

Next, we subtract 2 from both sides:

\[ t \geq 1 - 2 \] \[ t \geq -1 \]

Now we have our solution: \( t \geq -1 \).

Graphing the Solution

To graph \( t \geq -1 \):

1. Plot the endpoint: The endpoint is \( -1 \). Since the inequality is \( \geq \), we will use a closed circle at \( -1 \) to indicate that this point is included in the solution set.

2. Draw the ray: Since the inequality indicates that \( t \) can be greater than or equal to \( -1 \), we will draw a solid line (or ray) extending to the right from \( -1 \) towards positive infinity.

Here is how the graph looks:

• Closed circle at \( -1 \) (indicating it is included).
• Ray extending to the right.

Final Answer:

• The solution to the inequality is \( t \geq -1 \).
• The graph includes a closed circle at \( -1 \) and a ray extending to the right, representing \( t \) values greater than or equal to \( -1 \).