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The equation given is:

\[
8(x - 1) = 4(x + 3)
\]

### Step 1: Expand both sides
Distribute the constants on both sides of the equation:

\[
8(x - 1) = 8x - 8
\]
\[
4(x + 3) = 4x + 12
\]

So the equation becomes:

\[
8x - 8 = 4x + 12
\]

### Step 2: Move the terms involving \(x\) to one side
Subtract \(4x\) from both sides:

\[
8x - 4x - 8 = 12
\]
\[
4x - 8 = 12
\]

### Step 3: Solve for \(x\)
Add 8 to both sides:

\[
4x = 12 + 8
\]
\[
4x = 20
\]

Now, divide both sides by 4:

\[
x = \frac{20}{4} = 5
\]

### Solution:
\[
x = 5
\]

Would you like more details on any of the steps or have any questions?

Here are 5 related questions to practice:
1. How would the solution change if the equation were \( 8(x - 2) = 4(x + 1) \)?
2. What happens when you swap the coefficients on each side of the equation?
3. How can you check if your solution is correct?
4. Can you solve \( 3(x - 4) = 5(x + 2) \)?
5. What if you have an equation with fractions like \( \frac{3}{4}(x - 2) = \frac{5}{2}(x + 1) \)?

**Tip:** When solving linear equations, always aim to simplify both sides before moving terms across the equal sign.

Learn how to solve the linear equation 8(x - 1) = 4(x + 3) with a step-by-step guide. This problem involves applying the distributive property and solving for x. Perfect for students in Grades 7-8.

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