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The solution to the inequality \(-2\left(\frac{3x - 1}{3} - 1\right) + \frac{2}{3} > 0\) is:

\[
x < \frac{5}{3} \quad \text{or approximately} \quad x < 1.67
\]

This means that \(x\) can take any value less than \(\frac{5}{3}\).

Would you like more details or have any questions about this?

Here are five related questions for further practice:
1. How would the solution change if the inequality sign were reversed?
2. Can you solve a similar inequality: \(-3\left(\frac{2x - 4}{5} + 2\right) + \frac{4}{5} > 0\)?
3. How would the result differ if we add a constant term to both sides of the inequality?
4. What happens if the entire inequality is multiplied by a negative number?
5. Can you explain how the distributive property was used in solving this inequality?

**Tip**: Always remember to reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number!

Learn how to solve the inequality -2((3x-1)/3 - 1) + 2/3 > 0 step by step. This solution covers key algebraic concepts such as the distributive property and properties of inequalities. Suitable for students in Grades 8-10.

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