Let's solve the equation step by step:

Given equation:  
\[ 5(3x - 2) = 4(2x + 1) \]

### Step 1: Distribute the constants on both sides
Distribute the 5 on the left side and the 4 on the right side:

\[ 15x - 10 = 8x + 4 \]

### Step 2: Move the variable terms to one side
Subtract \(8x\) from both sides to get all the \(x\) terms on one side:

\[ 15x - 8x - 10 = 4 \]

This simplifies to:

\[ 7x - 10 = 4 \]

### Step 3: Move the constant terms to the other side
Add 10 to both sides to move the constant term to the right side:

\[ 7x = 14 \]

### Step 4: Solve for \(x\)
Finally, divide both sides by 7:

\[ x = 2 \]

The solution is \( x = 2 \).

Would you like more details on any of these steps or have any questions? 

Here are some related questions to consider:

1. How would you solve the equation if it included fractions?
2. What happens if the coefficients of \(x\) on both sides were equal?
3. How can you check if the solution \(x = 2\) is correct?
4. What if the equation had more than one variable?
5. How do you solve quadratic equations like \(ax^2 + bx + c = 0\)?

**Tip:** When solving linear equations, always move terms with the variable to one side and constants to the other to isolate the variable efficiently.

Discover how to solve the linear equation 5(3x - 2) = 4(2x + 1) with a comprehensive, step-by-step solution. This guide covers essential algebraic concepts and is suitable for students in Grades 6-8.

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