https://file.aiquickdraw.com/mathbot/file/1726586375988wlle6m96.jpg

Let's analyze the equation step by step and identify the error:

The original equation is:
\[
-4(3 - r) = 20
\]

### Step 1: Distribute the \(-4\) across the parentheses:
\[
-4 \cdot 3 + (-4) \cdot (-r) = -12 + 4r
\]
So, the equation becomes:
\[
-12 + 4r = 20
\]

### Step 2: Add 12 to both sides to isolate the \(4r\):
\[
4r = 20 + 12
\]
\[
4r = 32
\]

### Step 3: Divide both sides by 4:
\[
r = \frac{32}{4} = 8
\]

### Conclusion:
The solution should be \(r = 8\), not \(r = -8\).

Now, let's find the error in the choices:

- **A.** "The right side of the equation should be 8 after dividing each side by \(-4\)" — This is incorrect because dividing by \(-4\) would not yield 8.
- **B.** "The left side of the equation should be \(-12 + 4r\) after distributing" — This is correct because after distributing \(-4\), we get \(-12 + 4r\).
- **C.** "The left side of the equation should be \(-r\) after dividing each side by \(-4\)" — Incorrect, the left side becomes \(r = 8\).
- **D.** "The right side of the equation should be 8 after subtracting 12 from each side" — Incorrect, the right side should be 32 after adding 12 to both sides.

The correct answer is **B**.

Would you like further explanation on any part?

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Here are 5 related questions for practice:

1. How do you handle equations with parentheses and a negative sign outside the parentheses?
2. What is the effect of distributing a negative number across a parenthesis?
3. How do you isolate the variable in a linear equation step by step?
4. What happens when you divide both sides of an equation by a negative number?
5. How can you verify the solution to an algebraic equation?

**Tip**: Always double-check the distribution step in equations involving parentheses—it’s a common place for errors to occur.

The solution shown for the equation is incorrect. What is the correct solution? What is the error? -4(3-r) = 20

Learn how to solve the linear equation -4(3 - r) = 20 by distributing and isolating the variable r. Identify common errors in solving such equations and understand the correct steps involved. Suitable for Grades 7-8 students.

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