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The given equation is:

\[
\frac{2 - 3a}{-4} = \frac{-a + 5}{6}
\]

### Let's solve this step by step.

1. **Eliminate the denominators** by multiplying both sides of the equation by the least common denominator (LCD) of \(-4\) and \(6\), which is \(12\):

\[
12 \cdot \left(\frac{2 - 3a}{-4}\right) = 12 \cdot \left(\frac{-a + 5}{6}\right)
\]

Simplifying both sides:

\[
\left(12 \div -4\right)(2 - 3a) = \left(12 \div 6\right)(-a + 5)
\]

This simplifies to:

\[
-3(2 - 3a) = 2(-a + 5)
\]

2. **Expand both sides**:

\[
-3(2 - 3a) = -6 + 9a
\]
\[
2(-a + 5) = -2a + 10
\]

So now the equation becomes:

\[
-6 + 9a = -2a + 10
\]

3. **Move all terms involving \(a\) to one side** and constants to the other side:

\[
9a + 2a = 10 + 6
\]

Simplifying:

\[
11a = 16
\]

4. **Solve for \(a\)**:

\[
a = \frac{16}{11}
\]

Thus, the solution is:

\[
a = \frac{16}{11}
\]

Would you like further details or clarifications on any steps?

### Here are 5 questions to deepen understanding:
1. What happens if you change the signs in the equation?
2. How would you solve the equation if the denominators were different?
3. What would be the impact if the variables were squared?
4. How do you check if the solution is correct?
5. What if one side of the equation had a constant instead of a fraction?

**Tip:** Always simplify the equation step by step, ensuring you maintain balance by performing operations on both sides equally.

Discover how to solve the linear equation with fractions: (2 - 3a) / -4 = (-a + 5) / 6. This step-by-step solution involves algebraic manipulation, cross-multiplication, and balance techniques, suitable for students in Grades 8-10.

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