https://file.aiquickdraw.com/mathbot/file/1727938169826f8k3uvc1.jpg

Let's solve equation **5** from the image:

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

### Step 1: Eliminate the denominators
Find the least common denominator (LCD) of 4 and 3, which is 12. Multiply both sides of the equation by 12 to eliminate the fractions.

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

This simplifies to:

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

### Step 2: Simplify the expressions
Now distribute on both sides:

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

Simplify further:

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

### Step 3: Solve for \( t \)
Add \( 12t \) to both sides:

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

\[
13t - 18 = 8
\]

Now, add 18 to both sides:

\[
13t = 26
\]

Finally, divide by 13:

\[
t = 2
\]

### Solution:
\[
t = 2
\]

Let me know if you need further details or explanations!

Here are 5 related questions:
1. How can you check the solution by substituting back into the original equation?
2. What are some strategies for solving equations with fractions?
3. Can you derive the LCD if the denominators were more complex?
4. How does eliminating fractions make solving equations easier?
5. How can you apply this method to more complicated algebraic equations?

**Tip**: Always simplify your equation step by step, especially when dealing with multiple fractions.

This problem involves solving a linear equation with fractions: 3t/4 - 2t/3 = 2/3 - t. Follow the step-by-step solution, including eliminating fractions, using the distributive property, and combining like terms. Suitable for students in Grades 8-10.

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