Let's solve the equation step by step:

The given equation is:

\[
\frac{3t - 2}{4} - \frac{2t + 3}{3} = \frac{2}{3} - t
\]

### Step 1: Eliminate the fractions
To eliminate the denominators, multiply the entire equation by 12 (the least common denominator of 4 and 3).

\[
12 \times \left( \frac{3t - 2}{4} \right) - 12 \times \left( \frac{2t + 3}{3} \right) = 12 \times \left( \frac{2}{3} \right) - 12 \times t
\]

Simplifying each term:

\[
3(3t - 2) - 4(2t + 3) = 4(2) - 12t
\]

This becomes:

\[
9t - 6 - 8t - 12 = 8 - 12t
\]

### Step 2: Combine like terms
On the left side, combine the terms involving \( t \) and the constants:

\[
(9t - 8t) - (6 + 12) = 8 - 12t
\]

Simplifying further:

\[
t - 18 = 8 - 12t
\]

### Step 3: Isolate \( t \)
To isolate \( t \), add \( 12t \) to both sides:

\[
t + 12t - 18 = 8
\]

\[
13t - 18 = 8
\]

### Step 4: Solve for \( t \)
Now, add 18 to both sides:

\[
13t = 26
\]

Finally, divide by 13:

\[
t = \frac{26}{13} = 2
\]

### Final Answer:
\[
t = 2
\]

Would you like further details on any of the steps? 

Here are 5 related questions:
1. How do you handle equations with more complex fractions?
2. What if there were variables in the denominators?
3. Can you explain how to find the least common denominator in different cases?
4. How do you check if your solution is correct?
5. What other methods could solve this equation faster?

**Tip:** Always check your solution by substituting it back into the original equation to verify correctness.

This detailed guide walks through solving the linear equation 3t-2/4 - 2t+3/3 = 2/3-t step-by-step, using key algebraic concepts such as cross multiplication and combining like terms. This example is ideal for students in Grades 8-10 looking to master fractional equations.

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