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Let's solve the equation:

\[
3(x - 2) = 3x - 7
\]

1. Distribute the \(3\) on the left side:

\[
3x - 6 = 3x - 7
\]

2. Subtract \(3x\) from both sides:

\[
-6 = -7
\]

This is a contradiction because \(-6\) is not equal to \(-7\).

Therefore, **there are no solutions** to this equation.

Would you like further details or explanations? Here are some related questions:

1. What is a contradiction in algebra?
2. How can you identify when an equation has no solutions?
3. What are the possible types of solutions for linear equations?
4. How do you solve equations with variables on both sides?
5. What does it mean when an equation has infinite solutions?

**Tip:** When solving equations, always simplify both sides fully before trying to isolate the variable.

How many solutions does the equation 3(x - 2) = 3x - 7 have?

Learn how to determine the number of solutions for the linear equation 3(x - 2) = 3x - 7. This problem explores key algebraic concepts such as the distributive property and identifying contradictions in equations, making it suitable for students in Grades 7-9.

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