We are given the equation:

\[
\frac{x+1}{3} - \frac{2x - 3}{4} = 2
\]

Let's solve this step by step.

### Step 1: Eliminate the denominators
To eliminate the fractions, we can multiply through by the least common denominator (LCD) of 3 and 4, which is 12.

Multiply each term by 12:

\[
12 \times \left( \frac{x+1}{3} \right) - 12 \times \left( \frac{2x - 3}{4} \right) = 12 \times 2
\]

This simplifies to:

\[
4(x+1) - 3(2x - 3) = 24
\]

### Step 2: Expand the terms
Now distribute the constants:

\[
4x + 4 - 6x + 9 = 24
\]

### Step 3: Combine like terms
Combine the \(x\)-terms and constants on the left-hand side:

\[
(4x - 6x) + (4 + 9) = 24
\]

This simplifies to:

\[
-2x + 13 = 24
\]

### Step 4: Solve for \(x\)
Now, isolate \(x\). Subtract 13 from both sides:

\[
-2x = 24 - 13
\]

\[
-2x = 11
\]

Now divide both sides by \(-2\):

\[
x = \frac{11}{-2}
\]

\[
x = -\frac{11}{2}
\]

### Final Answer:
The solution to the equation is:

\[
x = -\frac{11}{2}
\]

Would you like a deeper explanation of any step?

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Here are 5 related questions to explore further:
1. What happens when both sides of the equation are fractions?
2. How can you check if the solution to a linear equation is correct?
3. What is the LCD, and why do we use it to eliminate fractions?
4. How would the process change if there were more than two terms in the equation?
5. Can this method be applied to equations involving variables in the denominator?

**Tip:** Always double-check your work by substituting the solution back into the original equation.

Learn how to solve the linear equation (x+1)/3 - (2x-3)/4 = 2 by eliminating fractions using the least common denominator (LCD). This detailed step-by-step solution covers key algebraic concepts and is ideal for students in Grades 8-10.

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