Question

Callie solved the equation below.

3x + 6(x – 7) = 4(3x + 6)

Which could be the correct first step in Callie's solution?

3x + 6x – 7 = 12x + 6

3x + 6x – 13 = 7x+ 10

3x + 6x + 42 = 12x + 24

3x + 6x– 42 = 12x + 24

Answer 1

To find the correct first step in Callie's solution, let's start with the original equation:

\[ 3x + 6(x - 7) = 4(3x + 6) \]

First, we will simplify both sides of the equation:

1. Distributing on the left side:
\[
6(x - 7) = 6x - 42
\]
So, the left side becomes:
\[
3x + 6x - 42
\]

2. Now, simplifying the left side:
\[
3x + 6x - 42 = 9x - 42
\]

3. For the right side, distribute \(4\):
\[
4(3x + 6) = 12x + 24
\]

Now the equation looks like this:
\[
9x - 42 = 12x + 24
\]

Now let's compare this to the provided options to find the matching first step:

1. **3x + 6x – 7 = 12x + 6**
- Incorrect. This does not match our simplification.

2. **3x + 6x – 13 = 7x + 10**
- Incorrect. This does not match our simplification.

3. **3x + 6x + 42 = 12x + 24**
- Incorrect. The left-hand side is incorrect.

4. **3x + 6x – 42 = 12x + 24**
- Correct! This is the equation we obtained after distributing.

Therefore, the correct first step in Callie's solution is:

**3x + 6x – 42 = 12x + 24**.