To solve the equation \( 5(n - 7) = 2(n + 14) \), follow these steps:

1. **Distribute** the numbers outside the parentheses:

\[
5 \cdot n - 5 \cdot 7 = 2 \cdot n + 2 \cdot 14
\]

This simplifies to:

\[
5n - 35 = 2n + 28
\]

2. **Move all the terms involving** \( n \) **to one side** of the equation and the constant terms to the other side:

\[
5n - 2n = 28 + 35
\]

This simplifies to:

\[
3n = 63
\]

3. **Solve for** \( n \) by dividing both sides by 3:

\[
n = \frac{63}{3} = 21
\]

So, the solution is \( n = 21 \).

Would you like further details, or do you have any questions about this solution?

Here are five related questions you might find useful:
1. How do you solve equations with variables on both sides?
2. What happens when there are no solutions to an equation?
3. How do you solve equations with more complex distributions?
4. What are the properties of equality used in solving linear equations?
5. How can you check your solution to a linear equation?

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

Discover how to solve the linear equation 5(n-7) = 2(n+14) with step-by-step instructions. This problem focuses on algebraic techniques, including the distributive property and simplifying equations. Ideal for students in Grades 7-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation