Question

12n+8
2
=
−2n+6

6n + 4
=
−2n + 6
+
2n
+
2n

Answer 1

To solve the equation step-by-step, it looks like we need to first simplify and then manipulate the given expressions. Let's clarify what the original setup seems to be and solve it systematically.

Starting with the first equation:

\[
12n + 8 = -2n + 6
\]

1. **Add \(2n\) to both sides:**
\[
12n + 2n + 8 = 6
\]
This simplifies to:
\[
14n + 8 = 6
\]

2. **Subtract 8 from both sides:**
\[
14n = 6 - 8
\]
This simplifies to:
\[
14n = -2
\]

3. **Now, divide both sides by 14:**
\[
n = \frac{-2}{14}
\]
Simplifying further:
\[
n = -\frac{1}{7}
\]

Now let's take the second equation you've written. You have

\[
6n + 4 = -2n + 6 + 2n + 2n
\]

1. **Combine the right side:**
\[
6n + 4 = -2n + 6 + 4n
\]
Simplifying gives us:
\[
6n + 4 = 2n + 6
\]

2. **Subtract \(2n\) from both sides:**
\[
6n - 2n + 4 = 6
\]
This simplifies to:
\[
4n + 4 = 6
\]

3. **Subtract 4 from both sides:**
\[
4n = 6 - 4
\]
This simplifies to:
\[
4n = 2
\]

4. **Now, divide both sides by 4:**
\[
n = \frac{2}{4}
\]
Simplifying further:
\[
n = \frac{1}{2}
\]

Thus, the solutions for the equations are:
- For the first equation: \( n = -\frac{1}{7} \)
- For the second equation: \( n = \frac{1}{2} \)