Question

Solve the equation and check your solution.



7n+6=4n−9

Answer 1

To solve the equation \( 7n + 6 = 4n - 9 \), follow these steps:

1. **Isolate the variable \( n \)** on one side of the equation. Start by subtracting \( 4n \) from both sides:

\[
7n - 4n + 6 = -9
\]
This simplifies to:

\[
3n + 6 = -9
\]

2. **Next, subtract 6 from both sides** to isolate the term with \( n \):

\[
3n = -9 - 6
\]
This simplifies to:

\[
3n = -15
\]

3. **Now divide both sides by 3** to solve for \( n \):

\[
n = \frac{-15}{3}
\]
Simplifying gives:

\[
n = -5
\]

Now that we have \( n = -5 \), we should check our solution by substituting \( n \) back into the original equation.

**Check:**

Substituting \( n = -5 \) into the left side of the equation:

\[
7(-5) + 6 = -35 + 6 = -29
\]

Now substituting \( n = -5 \) into the right side of the equation:

\[
4(-5) - 9 = -20 - 9 = -29
\]

Since both sides are equal:

\[
-29 = -29
\]

The solution \( n = -5 \) is confirmed to be correct. Thus, the final answer is:

\[
\boxed{-5}
\]