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Let's simplify the expression step by step.

The expression given is:

\[
\frac{2}{3}y - 2\left(\frac{4}{3}y + z\right)
\]

### Step 1: Distribute the \(-2\) across the terms inside the parentheses.

\[
-2 \times \frac{4}{3}y - 2 \times z = -\frac{8}{3}y - 2z
\]

### Step 2: Substitute the distributed terms back into the expression:

\[
\frac{2}{3}y - \left(\frac{8}{3}y + 2z\right)
\]

### Step 3: Combine the like terms involving \(y\):

\[
\left(\frac{2}{3}y - \frac{8}{3}y\right) - 2z = -\frac{6}{3}y - 2z
\]

\[
-\frac{6}{3}y - 2z = -2y - 2z
\]

### Final Simplified Expression:
\[
-2y - 2z
\]

This is the simplified form of the expression.

Would you like to go over any part of this in more detail?

### Relative Questions:
1. How would you factor the final expression \(-2y - 2z\)?
2. What happens if \(y\) and \(z\) are both equal to 1?
3. How would the expression change if the original constant outside the parentheses were \(+2\) instead of \(-2\)?
4. What are the implications of changing the sign in front of the \(\frac{4}{3}y\) inside the parentheses?
5. How would you apply this type of algebraic manipulation in a real-world context?

### Tip:
Always distribute negative signs carefully when simplifying algebraic expressions, as they often cause sign errors.

Simplify the expression: \(\frac{2}{3}y - 2\left(\frac{4}{3}y + z\right)\)

Discover how to simplify the algebraic expression \(\frac{2}{3}y - 2\left(\frac{4}{3}y + z\right)\). This step-by-step solution covers key algebraic concepts and is ideal for students in Grades 8-10.

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