https://file.aiquickdraw.com/mathbot/file/1726379744326poir7iha.jpg

The expression given in the image is:

\[
-2 - \frac{3}{4} x \cdot \frac{1}{5} - \left( -\frac{3}{5} x \cdot \frac{4}{6} \right)
\]

Now let's simplify this step by step.

### Step 1: Simplify the products
- For the term \(\frac{3}{4} x \cdot \frac{1}{5}\), multiply the fractions:

\[
\frac{3}{4} \cdot \frac{1}{5} = \frac{3 \times 1}{4 \times 5} = \frac{3}{20}
\]

So the second term becomes:
\[
- \frac{3}{20} x
\]

- For the term \(\frac{3}{5} x \cdot \frac{4}{6}\), multiply the fractions:

\[
\frac{3}{5} \cdot \frac{4}{6} = \frac{3 \times 4}{5 \times 6} = \frac{12}{30} = \frac{2}{5}
\]

The term inside the parentheses becomes:
\[
-\left( -\frac{2}{5} x \right)
\]
Which simplifies to:
\[
+\frac{2}{5} x
\]

### Step 2: Combine the terms
Now, the expression becomes:
\[
-2 - \frac{3}{20} x + \frac{2}{5} x
\]

### Step 3: Combine like terms
To combine \(-\frac{3}{20}x\) and \(\frac{2}{5}x\), we need a common denominator. The common denominator between 20 and 5 is 20.

Convert \(\frac{2}{5}\) to have a denominator of 20:
\[
\frac{2}{5} = \frac{8}{20}
\]

Now the expression is:
\[
-2 - \frac{3}{20}x + \frac{8}{20}x
\]

Combine the fractions:
\[
\frac{-3 + 8}{20}x = \frac{5}{20}x = \frac{1}{4}x
\]

### Final Answer:
\[
-2 + \frac{1}{4}x
\]

This is the simplified form of the expression.

Would you like further details or any clarifications?

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Here are five related questions:
1. How do you combine fractions with different denominators?
2. What are the steps to simplify expressions with parentheses?
3. What happens when you multiply two fractions?
4. How can you handle negative signs when simplifying algebraic expressions?
5. What is the significance of common denominators when adding or subtracting fractions?

**Tip:** Always make sure to distribute negative signs carefully when simplifying terms inside parentheses.

Learn how to simplify the algebraic expression -2 - 3/4 * x * 1/5 - (-3/5 * x * 4/6) with step-by-step calculations. This problem covers fraction multiplication, combining like terms, and simplifying algebraic expressions, making it suitable for students in Grades 6-8.

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