To solve the expression \(\left(\frac{2x}{3}\right)\left(x - \frac{2}{2}\right)\), let's follow the steps:

### Step 1: Simplify the expression inside the parentheses.
\[
x - \frac{2}{2} = x - 1
\]

So the expression now becomes:
\[
\left(\frac{2x}{3}\right)(x - 1)
\]

### Step 2: Distribute \(\frac{2x}{3}\) to both terms inside the parentheses.
\[
\frac{2x}{3} \times x - \frac{2x}{3} \times 1
\]

### Step 3: Perform the multiplication.
\[
\frac{2x^2}{3} - \frac{2x}{3}
\]

So, the final simplified expression is:
\[
\frac{2x^2}{3} - \frac{2x}{3}
\]

Would you like to explore further details or have any questions?

Here are five related questions you might find useful:
1. How would you factor the expression \(\frac{2x^2}{3} - \frac{2x}{3}\)?
2. What happens to the expression when \(x = 3\)?
3. How do you graph the function \(f(x) = \frac{2x^2}{3} - \frac{2x}{3}\)?
4. What is the derivative of \(f(x) = \frac{2x^2}{3} - \frac{2x}{3}\)?
5. How can you rewrite the expression using common denominators?

**Tip:** When simplifying algebraic expressions, always start by simplifying within parentheses and then apply the distributive property.

Learn how to simplify the expression (2x/3)(x - 1) step-by-step. This problem covers algebraic simplification and multiplication of algebraic expressions, suitable for Grades 7-9 students.

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