Let's check the solution for the equation:

\[
\frac{n}{2} - \frac{3n}{4} + \frac{5n}{6} = 21
\]

### Step 1: Find a common denominator
The denominators are \( 2 \), \( 4 \), and \( 6 \). The least common denominator (LCD) of these is \( 12 \). We'll express all terms with a denominator of 12.

- \(\frac{n}{2} = \frac{6n}{12}\)
- \(\frac{3n}{4} = \frac{9n}{12}\)
- \(\frac{5n}{6} = \frac{10n}{12}\)

### Step 2: Substitute and combine like terms
Now substitute these into the equation:

\[
\frac{6n}{12} - \frac{9n}{12} + \frac{10n}{12} = 21
\]

Combine the terms on the left-hand side:

\[
\frac{(6n - 9n + 10n)}{12} = 21
\]

\[
\frac{7n}{12} = 21
\]

### Step 3: Solve for \( n \)
To isolate \( n \), multiply both sides by 12:

\[
7n = 21 \times 12
\]

\[
7n = 252
\]

Now divide both sides by 7:

\[
n = \frac{252}{7} = 36
\]

### Step 4: Check the solution
Substitute \( n = 36 \) back into the original equation:

\[
\frac{36}{2} - \frac{3 \times 36}{4} + \frac{5 \times 36}{6} = 21
\]

Simplifying each term:

\[
18 - 27 + 30 = 21
\]

\[
21 = 21
\]

The solution checks out! The value of \( n \) is **36**.

Would you like more details on any step? Here are some related questions for further exploration:

1. How do you find the least common denominator (LCD) between fractions?
2. How do you simplify expressions involving fractions and variables?
3. What is the process for combining like terms in algebraic equations?
4. How do you check the correctness of a solution in algebra?
5. How can equations with fractions be solved efficiently?

**Tip:** Always check your solution by substituting the variable back into the original equation to ensure accuracy.

Learn how to solve the equation n/2 - 3n/4 + 5n/6 = 21 by finding a common denominator, combining like terms, and solving for n. This step-by-step solution covers key algebraic concepts, including working with fractions and solving linear equations. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation