Which of the following equations correctly represents solving Q=140−4PQ=140−4P for PP?

P=140−QP=140−Q

P=35−14QP=35−14Q

P=140−4QP=140−4Q

P=35−4QP=35−4Q

P=140+Q


Let's examine each of the options provided to determine which correctly represents solving \( Q = 140 - 4P \) for \( P \):

1. **\( P = 140 - Q \)**: This is incorrect because it doesn't correctly isolate \( P \). The equation \( Q = 140 - 4P \) needs to account for the coefficient of \( P \) when solving.

2. **\( P = 35 - \frac{1}{4}Q \)**: This is correct. If we solve \( Q = 140 - 4P \) for \( P \), dividing both sides by -4 after rearranging gives:
   \[
   P = \frac{140 - Q}{4} = 35 - \frac{1}{4}Q
   \]

3. **\( P = 140 - 4Q \)**: This is incorrect. The original equation has \( -4P \), so the correct manipulation should involve dividing by -4, not by 4.

4. **\( P = 35 - \frac{1}{4}Q \)**: This is correct. It matches the second option.

5. **\( P = 140 + Q \)**: This is incorrect. Adding \( Q \) doesn't correctly isolate \( P \) as per the original equation.

Therefore, the correct answer is:

\[
P = 35 - \frac{1}{4}Q
\]

Would you like further clarification, or do you have any other questions?

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Here are some related questions:

1. Why do we divide by -4 when solving for \( P \)?
2. Can you solve the equation using an alternative method?
3. How does the slope of a line relate to the coefficient of \( P \) in this context?
4. What are some common mistakes to avoid when solving linear equations?
5. How can this solution be interpreted in a real-world context?

**Tip:** Always double-check your solutions by plugging them back into the original equation.

Explore how to solve the equation Q = 140 - 4P for P with detailed steps and explanations. This problem involves linear equations and requires rearranging terms to isolate P correctly. Suitable for Grades 7-9 students and anyone interested in algebraic problem-solving.

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