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Let's go step by step through the solution shown in the image:

### Equation: 
\[ 2(x - 1) - 3(x + 2) = 8 - 4x \]

#### Step 1:
**Distribute the constants** to the terms inside the parentheses:
\[
2(x - 1) - 3(x + 2) = 2x - 2 - 3x - 6
\]
This simplifies to:
\[
2x - 2 - 3x - 6 = 8 - 4x
\]
**Reason**: Apply the distributive property \( a(b + c) = ab + ac \).

#### Step 2:
**Combine like terms** on the left side of the equation:
\[
(2x - 3x) + (-2 - 6) = -x - 8
\]
This gives:
\[
-x - 8 = 8 - 4x
\]
**Reason**: Combine like terms.

#### Step 3:
**Add \(4x\) to both sides** to eliminate the variable on the right:
\[
-x + 4x - 8 = 8
\]
This simplifies to:
\[
3x - 8 = 8
\]
**Reason**: Add \(4x\) to both sides to get all \(x\)-terms on one side.

#### Step 4:
**Add 8 to both sides** to isolate the term with \(x\):
\[
3x - 8 + 8 = 8 + 8
\]
This simplifies to:
\[
3x = 16
\]
**Reason**: Add 8 to both sides.

#### Step 5:
**Divide both sides by 3** to solve for \(x\):
\[
x = \frac{16}{3}
\]
This can also be written as:
\[
x = 5 \frac{1}{3}
\]
**Reason**: Divide both sides by 3.

### Final Answer:
\[
x = 5 \frac{1}{3}
\]

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Do you want any further clarification or details on a specific step?

### Related Questions:
1. How do you apply the distributive property to more complex expressions?
2. What are like terms, and how do you combine them?
3. Why is it important to isolate the variable when solving equations?
4. Can you solve an equation when the variable appears on both sides?
5. What are the different ways to represent fractions and mixed numbers?

### Tip:
Always check your solution by plugging the value of \(x\) back into the original equation to ensure it satisfies both sides.

Provide a reason for each step in solving the equation 2(x - 1) - 3(x + 2) = 8 - 4x

Learn how to solve the linear equation 2(x - 1) - 3(x + 2) = 8 - 4x with detailed step-by-step reasoning. This problem involves algebraic concepts such as the distributive property, combining like terms, and isolating variables. Suitable for students in Grades 8-10.

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