Let's solve the equation \( 0.1j = 2(0.3j + 0.5) \).

### Step 1: Distribute the 2 on the right side
First, distribute the 2 to both terms inside the parentheses:
\[
0.1j = 2 \times 0.3j + 2 \times 0.5
\]
This simplifies to:
\[
0.1j = 0.6j + 1
\]

### Step 2: Move all terms involving \( j \) to one side
Subtract \( 0.6j \) from both sides to isolate the \( j \) terms on one side:
\[
0.1j - 0.6j = 1
\]
This simplifies to:
\[
-0.5j = 1
\]

### Step 3: Solve for \( j \)
Divide both sides by \(-0.5\) to solve for \( j \):
\[
j = \frac{1}{-0.5} = -2
\]

### Final Answer:
\[
j = -2
\]

Would you like more details or have any questions?

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Here are some related questions:
1. How do you handle equations with decimal coefficients?
2. What if the decimals were more complex, like repeating decimals?
3. Can you explain the process of distributing and why it's important?
4. What if there were more terms in the parentheses?
5. How do you check your solution for accuracy?
6. Can this equation be solved graphically?
7. What happens if you multiply both sides by a factor first?
8. How would the solution change if the equation had negative coefficients?

**Tip:** When working with decimals in equations, you can eliminate them by multiplying the entire equation by a power of 10.

Learn how to solve the linear equation 0.1j = 2(0.3j + 0.5) step-by-step with detailed explanations and example calculations. This problem involves understanding linear equations and applying the distributive property to simplify expressions. Suitable for students in Grades 7-9.

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