Let's solve the equation \( \frac{1}{5}(5x - 5) + 3x = -9\left(\frac{1}{3}x + 4\right) \).

### Step 1: Distribute on both sides
First, distribute the \( \frac{1}{5} \) on the left side and the \( -9 \) on the right side:

\[
\frac{1}{5} \times 5x - \frac{1}{5} \times 5 + 3x = -9 \times \frac{1}{3}x - 9 \times 4
\]

This simplifies to:

\[
x - 1 + 3x = -3x - 36
\]

### Step 2: Combine like terms
Combine the \( x \) terms on both sides:

\[
4x - 1 = -3x - 36
\]

### Step 3: Move all terms involving \( x \) to one side
Add \( 3x \) to both sides to get all the \( x \) terms on one side:

\[
7x - 1 = -36
\]

### Step 4: Isolate the \( x \) term
Add \( 1 \) to both sides to isolate the term with \( x \):

\[
7x = -35
\]

### Step 5: Solve for \( x \)
Finally, divide both sides by 7:

\[
x = \frac{-35}{7} = -5
\]

So, the solution is \( x = -5 \).

Would you like more details or have any questions?

### Related Questions:
1. How do you solve equations with both fractions and distribution?
2. What is the importance of combining like terms in solving equations?
3. How do you check if your solution to an equation is correct?
4. What are some common pitfalls in solving linear equations?
5. How can you simplify complex equations before solving them?

### Tip:
Always distribute first before combining like terms—this ensures you simplify the equation correctly!

Learn how to solve the equation 1/5(5x-5) + 3x = -9(1/3x+4) with a detailed step-by-step solution. This problem covers key algebraic concepts including equations, distributive property, and solving linear equations. Suitable for students in Grades 7-9.

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