https://file.aiquickdraw.com/mathbot/file/1727397048226s2piy3tq.jpg

The equation shown in the image is:

\[
0.1j = 2(0.3j + 0.5)
\]

Let's solve this step by step.

### Step 1: Distribute the 2 on the right-hand side
\[
0.1j = 2 \times 0.3j + 2 \times 0.5
\]
\[
0.1j = 0.6j + 1
\]

### Step 2: Move all terms with \( j \) to one side of the equation
Subtract \( 0.6j \) from both sides:
\[
0.1j - 0.6j = 1
\]
\[
-0.5j = 1
\]

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

### Solution:
The value of \( j \) is \(-2\).

Would you like further details or have any questions?

Here are some related questions to explore further:
1. What is the method used to solve linear equations like this one?
2. How do you know when to distribute in an equation?
3. What happens if both sides of the equation have variables?
4. How can you check your solution for accuracy?
5. Are there other strategies for solving similar types of equations?

**Tip:** Always distribute first when parentheses are involved in an equation to simplify it for easier solving.

Learn how to solve the linear equation 0.1j = 2(0.3j + 0.5) using the distributive property and variable isolation. This problem is an excellent demonstration of basic algebraic techniques suitable for students in Grades 6-8.

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