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### Question 7:
#### Part (a) - Solve for \( C \) in the equation \( F = \frac{9}{5}C + 32 \)
Given the equation:
\[
F = \frac{9}{5}C + 32
\]
We want to solve for \( C \) (Celsius). Here's the step-by-step process:

1. Subtract 32 from both sides to isolate the \( \frac{9}{5}C \) term:
   \[
   F - 32 = \frac{9}{5}C
   \]

2. Multiply both sides of the equation by \( \frac{5}{9} \) to solve for \( C \):
   \[
   C = \frac{5}{9}(F - 32)
   \]

So, the formula to convert Fahrenheit to Celsius is:
\[
C = \frac{5}{9}(F - 32)
\]

#### Part (b) - Solve for \( r \) in the simple interest formula \( A = P + Prt \)
The given formula is:
\[
A = P + Prt
\]
We need to solve for \( r \). Let's simplify:

1. Subtract \( P \) from both sides:
   \[
   A - P = Prt
   \]

2. Divide both sides by \( Pt \) to isolate \( r \):
   \[
   r = \frac{A - P}{Pt}
   \]

Thus, the formula for \( r \) is:
\[
r = \frac{A - P}{Pt}
\]

### Question 8:
We are asked to factor each expression by pulling out the greatest common factor (GCF).

#### Part (a) - Factor \( 3x + 6 \)
The GCF of \( 3x \) and \( 6 \) is 3. Factor out 3:
\[
3x + 6 = 3(x + 2)
\]

#### Part (b) - Factor \( 20x - 8 \)
The GCF of \( 20x \) and \( -8 \) is 4. Factor out 4:
\[
20x - 8 = 4(5x - 2)
\]

#### Part (c) - Factor \( x^2 - 4x \)
The GCF of \( x^2 \) and \( -4x \) is \( x \). Factor out \( x \):
\[
x^2 - 4x = x(x - 4)
\]

#### Part (d) - Factor \( 4x^2 + 4x \)
The GCF of \( 4x^2 \) and \( 4x \) is \( 4x \). Factor out \( 4x \):
\[
4x^2 + 4x = 4x(x + 1)
\]

### Question 9:
We are asked to solve the simple interest formula \( A = P + Prt \) for \( P \) by using factoring.

The formula is:
\[
A = P + Prt
\]

1. Factor out \( P \) from the right-hand side:
   \[
   A = P(1 + rt)
   \]

2. Divide both sides by \( (1 + rt) \) to solve for \( P \):
   \[
   P = \frac{A}{1 + rt}
   \]

Thus, the formula for \( P \) is:
\[
P = \frac{A}{1 + rt}
\]

---

Do you want further details or have any questions on these steps?

Here are 5 related questions for practice:
1. How would you solve the equation \( F = \frac{9}{5}C + 32 \) if \( F = 68^\circ F \)?
2. What would be the value of \( r \) in the formula \( A = P + Prt \) if \( A = 1200 \), \( P = 1000 \), and \( t = 2 \)?
3. How do you factor \( 6x + 9 \)?
4. How do you factor \( 15x^2 - 5x \)?
5. How would you solve the equation \( A = P + Prt \) for \( t \)?

**Tip:** Always look for the greatest common factor (GCF) first when factoring expressions to simplify your work!

Solve for the specified variable in each equation and factor expressions by the Greatest Common Factor (GCF). Includes solving for Celsius in F = (9/5)C + 32, solving for r in the simple interest formula A = P + Prt, and factoring algebraic expressions.

Learn how to solve for Celsius in F = (9/5)C + 32, find the interest rate in the simple interest formula A = P + Prt, and factor algebraic expressions by the Greatest Common Factor (GCF). Detailed step-by-step explanations provided.

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