Let's solve the equation \( 14 + 3n = 5n - 6 \) for \( n \).

### Step 1: Move all terms involving \( n \) to one side of the equation.
We can do this by subtracting \( 3n \) from both sides:

\[
14 = 5n - 3n - 6
\]

### Step 2: Simplify the equation.
Combine like terms:

\[
14 = 2n - 6
\]

### Step 3: Move the constant term to the other side.
Add \( 6 \) to both sides of the equation:

\[
14 + 6 = 2n
\]

\[
20 = 2n
\]

### Step 4: Solve for \( n \).
Divide both sides by 2:

\[
n = \frac{20}{2}
\]

\[
n = 10
\]

So, the solution is \( n = 10 \).

Would you like details on this process or have any questions? Here are some related questions:

1. How do you solve equations with variables on both sides?
2. What are the steps to isolate a variable in an equation?
3. Can you solve for \( n \) if the equation were \( 4n + 7 = 2n + 19 \)?
4. How does moving terms across the equals sign affect the equation?
5. What happens if there are no solutions to an equation?

**Tip:** Always check your solution by substituting it back into the original equation.

Learn how to solve the equation 14 + 3n = 5n - 6 with a detailed step-by-step solution. This problem covers key algebraic concepts, including solving linear equations. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation