https://file.aiquickdraw.com/mathbot/file/172743359425727ixwm5g.jpg

The equation in the image is:

\[
2x + \frac{3x - 1}{2} = 2 + \frac{5x - 2}{3}
\]

Let's solve this step by step.

### Step 1: Eliminate the fractions
We can eliminate the fractions by multiplying the entire equation by 6 (the least common denominator of 2 and 3).

\[
6 \left( 2x + \frac{3x - 1}{2} \right) = 6 \left( 2 + \frac{5x - 2}{3} \right)
\]

This simplifies to:

\[
12x + 3(3x - 1) = 12 + 2(5x - 2)
\]

### Step 2: Expand both sides
Expand the terms on both sides:

\[
12x + 9x - 3 = 12 + 10x - 4
\]

Simplify further:

\[
21x - 3 = 10x + 8
\]

### Step 3: Isolate the variable
Move all terms involving \( x \) to one side and constant terms to the other side:

\[
21x - 10x = 8 + 3
\]

\[
11x = 11
\]

### Step 4: Solve for \( x \)
Divide both sides by 11:

\[
x = 1
\]

The solution to the equation is \( x = 1 \).

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

---

Here are five related questions to practice:

1. How would you solve an equation with three fractions on both sides?
2. What is the benefit of finding the least common denominator in equations with fractions?
3. How would you verify the solution to this equation by substitution?
4. How can multiplying both sides of an equation help simplify it?
5. What happens if an equation has no solution, and how do you identify such cases?

**Tip**: When solving equations with fractions, always aim to eliminate fractions early by multiplying through by the least common denominator.

Solve the equation: 2x + (3x - 1)/2 = 2 + (5x - 2)/3

Learn how to solve the linear equation 2x + (3x - 1)/2 = 2 + (5x - 2)/3 step-by-step. This problem involves eliminating fractions and solving for x, making it ideal for high school students in Grades 9-10.

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