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Let's solve the given equation step-by-step. The equation is:

\[
5(3x + 5) = 6(4x + 5)
\]

### Step 1: Distribute both sides of the equation.

On the left side:
\[
5(3x + 5) = 5 \cdot 3x + 5 \cdot 5 = 15x + 25
\]

On the right side:
\[
6(4x + 5) = 6 \cdot 4x + 6 \cdot 5 = 24x + 30
\]

Now the equation becomes:
\[
15x + 25 = 24x + 30
\]

### Step 2: Rearrange the equation to get all terms involving \(x\) on one side and the constant terms on the other side.

First, subtract \(15x\) from both sides:
\[
25 = 9x + 30
\]

Next, subtract 30 from both sides:
\[
25 - 30 = 9x
\]
\[
-5 = 9x
\]

### Step 3: Solve for \(x\).

Divide both sides by 9:
\[
x = \frac{-5}{9}
\]

Thus, the solution is:
\[
x = \frac{-5}{9}
\]

Would you like any further explanation? 

Here are five related questions to explore:

1. How would the solution change if the equation were \(5(3x + 7) = 6(4x + 5)\)?
2. Can you solve a similar equation involving a negative coefficient, such as \(7(3x - 4) = 5(2x + 8)\)?
3. What happens if you multiply both sides of the equation by a constant before distributing?
4. How can you check if your solution to a linear equation is correct?
5. What is the general process for solving linear equations that involve fractions?

**Tip:** Always simplify both sides of the equation before moving terms across the equals sign to avoid mistakes.

Solve the equation for the given variable: 5(3x + 5) = 6(4x + 5). If your answer is a fraction, write it in reduced fractional form.

Learn how to solve the linear equation 5(3x + 5) = 6(4x + 5) with a clear, step-by-step explanation. The solution involves applying the distributive property and isolating the variable x. Suitable for students in Grades 6-8.

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