Question

Put the steps in order to solve the equation: 3n+9+4n=2 (6 points) Step 1:combine like terms divide both sides by 7 ,use subtraction to get the inverse operation, to get 7n=-7,n=1,7n+9=2. Step 2:combine like terms divide both sides by 7 ,use subtraction to get the inverse operation, to get 7n=-7,n=1,7n+9=2. Step 3: combine like terms divide both sides by 7 ,use subtraction to get the inverse operation, to get 7n=-7,n=1,7n+9=2

Answer 1

It looks like the steps provided have some repetition and unclear phrasing. Let’s clarify and organize the steps to solve the equation \( 3n + 9 + 4n = 2 \):

1. **Combine Like Terms**: Start by combining \( 3n \) and \( 4n \) on the left side of the equation.
\[
3n + 4n + 9 = 2 \quad \Rightarrow \quad 7n + 9 = 2
\]

2. **Use Subtraction to Isolate the Variable**: Subtract \( 9 \) from both sides to isolate the term with the variable \( n \).
\[
7n + 9 - 9 = 2 - 9 \quad \Rightarrow \quad 7n = -7
\]

3. **Divide Both Sides by 7**: Divide both sides by \( 7 \) to solve for \( n \).
\[
n = \frac{-7}{7} \quad \Rightarrow \quad n = -1
\]

So the corrected and sequenced steps are:

1. Combine Like Terms: \( 3n + 9 + 4n = 2 \) becomes \( 7n + 9 = 2 \).
2. Subtract \( 9 \) from both sides: \( 7n = -7 \).
3. Divide by \( 7 \): \( n = -1 \).

The final solutions can be verified:
Substituting \( n = -1 \):
\[
3(-1) + 9 + 4(-1) = -3 + 9 - 4 = 2
\]
It holds true!