https://file.aiquickdraw.com/mathbot/file/1727709488912w9qmhofm.jpg

Let's solve the equation step-by-step:

The given equation is:

\[
-4(x - 2) = 5(3x - 8)
\]

### Step 1: Distribute on both sides

#### Left side:
Distribute the \(-4\) across \((x - 2)\):

\[
-4(x - 2) = -4x + 8
\]

#### Right side:
Distribute the \(5\) across \((3x - 8)\):

\[
5(3x - 8) = 15x - 40
\]

### Step 2: Combine both sides

So, the equation becomes:

\[
-4x + 8 = 15x - 40
\]

This matches option **A**: \(-4x + 8 = 15x - 40\), which is the correct answer.

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Do you have any further questions or want a detailed explanation of any part?

### Related Questions:
1. How do you solve for \(x\) in this equation?
2. What are the next steps after distributing both sides?
3. Can this equation be solved graphically?
4. How would this equation look if you factored both sides?
5. What happens if you add \(4x\) to both sides?

#### Tip:
Always distribute carefully and handle signs (positive/negative) with attention to avoid errors.

Which of the following shows the equation after both sides have been distributed correctly? -4(x - 2) = 5(3x - 8)

Learn how to solve the linear equation -4(x - 2) = 5(3x - 8) by distributing both sides of the equation and simplifying. This algebra problem uses the distributive property and is appropriate for Grade 8 students.

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