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The equation you've provided is:

\[
\frac{6 - 3x}{3} - \frac{5x + 12}{4} = -1
\]

Let's solve this step by step.

### Step 1: Simplify the fractions.
For the first term:

\[
\frac{6 - 3x}{3} = \frac{6}{3} - \frac{3x}{3} = 2 - x
\]

So, the equation becomes:

\[
2 - x - \frac{5x + 12}{4} = -1
\]

### Step 2: Eliminate the fraction by multiplying the entire equation by 4 (the denominator of the second term).

Multiplying through by 4:

\[
4(2 - x) - (5x + 12) = 4(-1)
\]

This simplifies to:

\[
8 - 4x - 5x - 12 = -4
\]

### Step 3: Combine like terms.

\[
(8 - 12) - (4x + 5x) = -4
\]

This becomes:

\[
-4 - 9x = -4
\]

### Step 4: Solve for \( x \).

Add 4 to both sides:

\[
-9x = 0
\]

Now, divide by -9:

\[
x = 0
\]

### Final Solution:

The solution to the equation is \( x = 0 \).

Would you like further explanation on any of the steps? Here are five related questions to deepen understanding:

1. What are the general steps for solving equations with fractions?
2. How can multiplying by a common denominator simplify equations?
3. What is the importance of combining like terms in algebraic equations?
4. How do we verify if \( x = 0 \) is the correct solution?
5. Can you explain why distributing is important when solving equations?

**Tip:** Always double-check your final solution by plugging it back into the original equation to ensure it satisfies the equation!

Solve the equation: (6 - 3x)/3 - (5x + 12)/4 = -1

This tutorial provides a step-by-step solution to the linear equation (6 - 3x)/3 - (5x + 12)/4 = -1, covering key concepts such as simplifying fractions and solving linear equations. Ideal for students in Grades 8-10.

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