2x-3 4x-2 6x-2 ------ + -------- - 2 = -------- 9 7 4

Let's solve the equation:

\[
\frac{2x - 3}{9} + \frac{4x - 2}{7} - 2 = \frac{6x - 2}{4}
\]

### Step 1: Clear the fractions
To eliminate the fractions, find the least common multiple (LCM) of the denominators: 9, 7, and 4. The LCM of 9, 7, and 4 is 252. Multiply every term by 252 to clear the fractions:

\[
252 \times \left(\frac{2x - 3}{9}\right) + 252 \times \left(\frac{4x - 2}{7}\right) - 252 \times 2 = 252 \times \left(\frac{6x - 2}{4}\right)
\]

### Step 2: Simplify each term
\[
28 \times (2x - 3) + 36 \times (4x - 2) - 504 = 63 \times (6x - 2)
\]

### Step 3: Distribute and simplify
\[
56x - 84 + 144x - 72 - 504 = 378x - 126
\]

Combine like terms on the left side:

\[
200x - 660 = 378x - 126
\]

### Step 4: Isolate \(x\)
Move all terms involving \(x\) to one side of the equation and constant terms to the other side:

\[
200x - 378x = -126 + 660
\]

\[
-178x = 534
\]

### Step 5: Solve for \(x\)
\[
x = \frac{534}{-178}
\]

Simplify the fraction:

\[
x = -3
\]

The solution is \( x = -3 \).

Would you like a detailed explanation of any steps, or do you have any questions?

### Relative Questions:
1. How do you find the least common multiple (LCM) of several numbers?
2. What are the steps to isolate a variable in an algebraic equation?
3. How do you handle equations with fractions?
4. What is the process for distributing and combining like terms?
5. How do you simplify fractions to their lowest terms?

### Tip:
When working with equations that involve fractions, multiplying through by the least common multiple of the denominators can simplify the process significantly.

Learn how to solve the equation involving fractions: (2x - 3) / 9 + (4x - 2) / 7 - 2 = (6x - 2) / 4 with a detailed step-by-step solution. This problem covers equations with fractions and requires knowledge of the least common multiple (LCM). Suitable for students in Grades 9-12.

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