https://file.aiquickdraw.com/mathbot/file/17267603355336m119ovg.jpg

Let's go over a couple of questions from the image you uploaded.

1. **Question 39:** Solve the equation.
   \[
   5(x - 2) - 4(3x + 5) = 97
   \]
   **Solution:**

   First, distribute the constants on both sides:
   \[
   5(x - 2) = 5x - 10
   \]
   \[
   -4(3x + 5) = -12x - 20
   \]
   The equation becomes:
   \[
   5x - 10 - 12x - 20 = 97
   \]
   Combine like terms:
   \[
   -7x - 30 = 97
   \]
   Add 30 to both sides:
   \[
   -7x = 127
   \]
   Divide by -7:
   \[
   x = \frac{127}{-7} = -18.14
   \]

---

2. **Question 40:** Solve the equation.
   \[
   -2(3y - 6) + 4(5y - 8) = 92
   \]
   **Solution:**

   First, distribute the constants:
   \[
   -2(3y - 6) = -6y + 12
   \]
   \[
   4(5y - 8) = 20y - 32
   \]
   The equation becomes:
   \[
   -6y + 12 + 20y - 32 = 92
   \]
   Combine like terms:
   \[
   14y - 20 = 92
   \]
   Add 20 to both sides:
   \[
   14y = 112
   \]
   Divide by 14:
   \[
   y = 8
   \]

---

Would you like me to solve more questions or provide explanations for these steps?

Here are 5 related problems to think about:
1. Solve \( 3(2x + 5) - 4(3x + 2) = 10 \).
2. How would the solution change if there were no constants on the right-hand side?
3. Try solving \( 7x - 3(x - 4) = 24 \).
4. What happens if you reverse the signs inside the parentheses for equation 39?
5. Solve \( 2x - 5 = 3(x + 1) \) and compare its solution steps with problem 39.

**Tip:** Always simplify both sides of an equation before moving variables to one side.

Solve the equations: 1) 5(x - 2) - 4(3x + 5) = 97, 2) -2(3y - 6) + 4(5y - 8) = 92

Learn how to solve linear equations involving the distributive property, such as 5(x - 2) - 4(3x + 5) = 97 and -2(3y - 6) + 4(5y - 8) = 92. This lesson covers key algebraic concepts and methods used to simplify and solve equations. Suitable for students in Grades 7-9.

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