https://file.aiquickdraw.com/mathbot/file/1729539325363qxkhuyoa.jpg

The problem shown in the image is to evaluate the expression \( x - 3y \) when:

- \( x = -\frac{2}{3} \)
- \( y = \frac{4}{5} \)

Let's break it down step by step:

1. **Substitute the values of \( x \) and \( y \) into the expression**:
   \[
   x - 3y = -\frac{2}{3} - 3 \times \frac{4}{5}
   \]

2. **Simplify the multiplication**:
   \[
   3 \times \frac{4}{5} = \frac{12}{5}
   \]
   Now the expression becomes:
   \[
   -\frac{2}{3} - \frac{12}{5}
   \]

3. **Find a common denominator** to subtract the fractions. The least common denominator (LCD) between 3 and 5 is 15. Convert both fractions:
   \[
   -\frac{2}{3} = -\frac{10}{15}, \quad \frac{12}{5} = \frac{36}{15}
   \]
   Now the expression is:
   \[
   -\frac{10}{15} - \frac{36}{15}
   \]

4. **Subtract the fractions**:
   \[
   -\frac{10}{15} - \frac{36}{15} = -\frac{46}{15}
   \]

So, the final simplified result is:
\[
x - 3y = -\frac{46}{15}
\]

Would you like further details or explanations? 

Here are some additional related questions to expand on this topic:
1. What is the process of finding a common denominator?
2. How do you simplify fractions after addition or subtraction?
3. What are the rules for multiplying fractions?
4. How can you convert improper fractions to mixed numbers?
5. What is the difference between improper fractions and mixed fractions?

**Tip**: Always check the denominators when adding or subtracting fractions—finding the least common denominator simplifies the process.

Evaluate the expression when x = -2/3 and y = 4/5 for the equation x - 3y.

Learn how to evaluate the algebraic expression x - 3y when x = -2/3 and y = 4/5 with this detailed step-by-step solution. This problem covers key concepts in algebra, including fraction multiplication, finding a common denominator, and simplifying expressions. Suitable for students in Grades 6-8.

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