To solve the equation \( \frac{3}{10} \times \frac{-2}{5} = 2 \), let's follow these steps:

### Step 1: Multiply the fractions on the left side
The multiplication of two fractions is done by multiplying their numerators and denominators:

\[
\frac{3}{10} \times \frac{-2}{5} = \frac{3 \times -2}{10 \times 5} = \frac{-6}{50}
\]

So, the equation becomes:

\[
\frac{-6}{50} = 2
\]

### Step 2: Simplify the fraction
The fraction \( \frac{-6}{50} \) can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:

\[
\frac{-6}{50} = \frac{-3}{25}
\]

So the equation now becomes:

\[
\frac{-3}{25} = 2
\]

### Step 3: Solve the equation
To solve for \( x \), we need to eliminate the fraction by multiplying both sides of the equation by 25:

\[
-3 = 2 \times 25
\]

\[
-3 = 50
\]

This is a contradiction, meaning no real solution exists for this equation. The equation is inconsistent.

Would you like more details or have any questions?

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Here are five related questions:
1. How do you handle equations with multiple fractions?
2. What does it mean when an equation has no solution?
3. Can this equation be adjusted to have a solution?
4. How can we represent contradictions in algebra?
5. How can you check if an equation has infinitely many solutions?

**Tip:** Always simplify fractions early in an equation to avoid unnecessary complexity!

This page walks through the solution for the equation 3/10 × -2/5 = 2, including steps on multiplying fractions and identifying when an equation has no real solution. Learn how to simplify fractions and solve algebraic inconsistencies, suitable for students in Grades 6-8.

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