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Let's solve the equation:

\[
3(4r + 5) - 2(3r + 4) = 7
\]

### Step-by-step solution:

1. **Distribute the terms:**
   \[
   3(4r + 5) = 12r + 15
   \]
   \[
   -2(3r + 4) = -6r - 8
   \]

   Now the equation becomes:
   \[
   12r + 15 - 6r - 8 = 7
   \]

2. **Combine like terms:**
   \[
   (12r - 6r) + (15 - 8) = 7
   \]
   \[
   6r + 7 = 7
   \]

3. **Isolate \( r \):**
   Subtract 7 from both sides:
   \[
   6r = 0
   \]

4. **Solve for \( r \):**
   \[
   r = 0
   \]

So, the solution is \( r = 0 \).

Would you like further clarification on any steps or more details?

### Related Questions:
1. How do you handle distribution in equations with parentheses?
2. What are like terms and how do you combine them?
3. What methods can you use to isolate the variable in an equation?
4. How do you verify if your solution to an equation is correct?
5. What happens when all terms cancel out in an equation?

**Tip:** Always simplify expressions on both sides before moving to solve the equation—it reduces errors and makes solving easier!

Solve for r in the equation: 3(4r + 5) - 2(3r + 4) = 7

Learn how to solve the linear equation 3(4r + 5) - 2(3r + 4) = 7 with a detailed step-by-step solution. This problem involves using the distributive property and combining like terms. Suitable for students in Grades 8-10.

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