Solve for 
\[t\].
 
\[16-2t=\dfrac{3}2t+9\]

To solve for \( t \) in the equation:

\[
16 - 2t = \frac{3}{2}t + 9
\]

we'll follow these steps:

### Step 1: Clear the equation of fractions
Multiply both sides by 2 to eliminate the fraction:

\[
2 \cdot (16 - 2t) = 2 \cdot \frac{3}{2}t + 2 \cdot 9
\]

This simplifies to:

\[
32 - 4t = 3t + 18
\]

### Step 2: Move all terms involving \( t \) to one side
Add \( 4t \) to both sides to bring the \( t \) terms together:

\[
32 = 7t + 18
\]

### Step 3: Isolate the \( t \) term
Subtract 18 from both sides:

\[
14 = 7t
\]

### Step 4: Solve for \( t \) by dividing both sides by 7:

\[
t = 2
\]

### Solution
The solution is:

\[
t = 2
\]

Would you like more details or have any questions about the steps?

---

Here are some questions to explore further:
1. What happens if we have more terms involving \( t \) on both sides?
2. How would the solution process change if there were more fractions?
3. Can we verify the solution by substituting \( t = 2 \) back into the original equation?
4. What is the process if we need to solve for another variable in a similar equation?
5. How can we approach equations with more complex terms, like polynomials?

**Tip:** When you encounter fractions, consider clearing them early by multiplying both sides by a common multiple. This often simplifies the solving process.

Solve for \( t \) in the equation: \( 16 - 2t = \frac{3}{2}t + 9 \).

Discover a step-by-step solution for solving the linear equation 16 - 2t = (3/2)t + 9. This guide covers clearing fractions, isolating variables, and solving for t, essential concepts in Algebra. Ideal for students in Grades 7-9.

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