https://file.aiquickdraw.com/mathbot/file/1725920684843q8xj8h4t.jpg

The equation you uploaded is:

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

Let's solve for \(x\).

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

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

This simplifies to:

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

### Step 2: Distribute the terms
Now distribute the 3 and the 4:

\[
3x + 6 - 4x + 4 = 24
\]

### Step 3: Combine like terms
Combine the \(x\)-terms and the constant terms:

\[
(3x - 4x) + (6 + 4) = 24
\]
\[
-x + 10 = 24
\]

### Step 4: Solve for \(x\)
Now subtract 10 from both sides:

\[
-x = 24 - 10
\]
\[
-x = 14
\]

Finally, multiply both sides by -1:

\[
x = -14
\]

Thus, the solution is \(x = -14\).

Would you like a detailed explanation or have any questions?

### Related Questions:
1. How do you handle equations with variables on both sides?
2. What is the significance of finding the least common denominator in equations with fractions?
3. How do you verify the solution of a linear equation?
4. How do distributive properties help in solving algebraic equations?
5. What would happen if you incorrectly combine terms during simplification?

### Tip:
Always remember to double-check your final answer by substituting it back into the original equation to ensure it's correct.

Solve the equation: (x + 2)/4 - (x - 1)/3 = 2

Discover how to solve the linear equation (x + 2)/4 - (x - 1)/3 = 2 using the least common denominator (LCD) method. This guide walks through the process of simplifying and solving the equation step-by-step, making it ideal for students in Grades 7-9.

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