Let's solve the equation step-by-step:

Given:

\[
2(X - 1) + 3X = 3
\]

### Step 1: Expand the equation

Distribute \(2\) to the terms inside the parentheses:

\[
2X - 2 + 3X = 3
\]

### Step 2: Combine like terms

Combine \(2X\) and \(3X\):

\[
5X - 2 = 3
\]

### Step 3: Isolate the variable term

Add \(2\) to both sides:

\[
5X = 5
\]

### Step 4: Solve for \(X\)

Divide both sides by \(5\):

\[
X = 1
\]

### Conclusion

The solution to the equation is:

\[
X = 1
\]

Would you like more details or have any questions?

### Related Questions:

1. How would the solution change if the equation was \(2(X + 1) + 3X = 3\)?
2. How can we solve for \(X\) if the equation is quadratic instead?
3. What happens if we add another variable to the equation?
4. How can we check if our solution is correct by substituting it back into the original equation?
5. How can this method be applied to solve inequalities?

### Tip:

Always double-check your solution by substituting it back into the original equation to ensure it satisfies the given equation.

Learn how to solve the equation 2(X-1) + 3X = 3 with a detailed step-by-step solution. This problem covers key algebraic concepts such as equations, distributive property, combining like terms, and isolating variables. Suitable for students in Grades 7-9.

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