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Let's first solve the inequality \( 2t + 9 \geq 5 \).

### Step 1: Isolate the variable \( t \)
We start by subtracting 9 from both sides of the inequality:
\[
2t + 9 - 9 \geq 5 - 9
\]
\[
2t \geq -4
\]

### Step 2: Solve for \( t \)
Now, divide both sides by 2:
\[
t \geq \frac{-4}{2}
\]
\[
t \geq -2
\]

### Solution:
The inequality is \( t \geq -2 \).

### Step 3: Graph the solution
- We place a **closed circle** at \( t = -2 \), because the inequality includes \( t = -2 \) (the "greater than or equal to" sign).
- The solution includes all values greater than or equal to \( -2 \), so we shade the number line to the **right** of \( -2 \).

### Final Graph:
- A closed circle at \( -2 \), with an arrow extending to the right, indicating \( t \geq -2 \).

Would you like further clarification or additional details? 

Here are five related questions to deepen your understanding:
1. How would the graph look if the inequality was \( t > -2 \) instead of \( t \geq -2 \)?
2. How would you solve and graph the inequality \( 3t - 4 \leq 7 \)?
3. What is the solution for the compound inequality \( -3 \leq t + 2 < 5 \)?
4. How would you graph a solution on a number line where \( t \leq -2 \)?
5. Can you explain how inequalities with absolute values are solved?

**Tip:** When graphing inequalities, remember that a closed circle is used for \( \geq \) or \( \leq \), while an open circle is used for \( > \) or \( < \).

Solve the inequality and graph the solution: 2t + 9 ≥ 5.

Learn how to solve and graph the linear inequality 2t + 9 ≥ 5 step-by-step. This solution demonstrates key algebra concepts, including isolating variables and graphing with closed circles on a number line. Suitable for Grades 6-8 students.

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