To solve the equation \( p(x - \frac{2}{5}) = -x + q \) for \( x \), we'll isolate \( x \) in terms of \( p \) and \( q \).

### Step 1: Distribute \( p \) on the left side
\[ p(x - \frac{2}{5}) = p \cdot x - p \cdot \frac{2}{5} \]
This simplifies to:
\[ p \cdot x - \frac{2p}{5} = -x + q \]

### Step 2: Move all terms involving \( x \) to one side
Add \( x \) to both sides:
\[ p \cdot x + x = q + \frac{2p}{5} \]

### Step 3: Factor out \( x \) on the left side
\[ x(p + 1) = q + \frac{2p}{5} \]

### Step 4: Solve for \( x \)
Divide both sides by \( (p + 1) \):
\[ x = \frac{q + \frac{2p}{5}}{p + 1} \]

### Final Answer
The solution for \( x \) is:
\[ x = \frac{q + \frac{2p}{5}}{p + 1} \]

Would you like more details, or do you have any questions about the steps?

Here are 5 questions related to this solution:
1. How do you simplify expressions with fractions like \(\frac{2p}{5}\)?
2. What happens if \( p = -1 \) in the equation?
3. Can you solve for \( q \) in terms of \( x \) and \( p \)?
4. What if \( p \) or \( q \) is a complex number?
5. How would you graph the equation \( p(x - \frac{2}{5}) = -x + q \)?

**Tip:** Always check if any values of the variables could lead to undefined expressions, like dividing by zero.

Learn how to solve the linear equation p(x - 2/5) = -x + q step-by-step with detailed explanations. This problem involves algebraic concepts like linear equations and fraction operations. Suitable for students in Grades 7-9.

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