Let's solve the equation step by step.

The given equation is:

\[
\frac{1}{2}(4n - 6) = \frac{1}{3}(9n + 12)
\]

### Step 1: Distribute the fractions on both sides.

Distribute \(\frac{1}{2}\) on the left side:

\[
\frac{1}{2} \times 4n - \frac{1}{2} \times 6 = 2n - 3
\]

Distribute \(\frac{1}{3}\) on the right side:

\[
\frac{1}{3} \times 9n + \frac{1}{3} \times 12 = 3n + 4
\]

So, the equation simplifies to:

\[
2n - 3 = 3n + 4
\]

### Step 2: Move the variable terms to one side of the equation.

Subtract \(2n\) from both sides:

\[
-3 = n + 4
\]

### Step 3: Move the constant term to the other side of the equation.

Subtract 4 from both sides:

\[
n = -7
\]

### Final Answer:
The solution to the equation is \(n = -7\).

Would you like more details or have any questions? Here are some related questions for further practice:

1. Solve the equation \(\frac{1}{4}(8n - 12) = \frac{1}{2}(4n + 6)\).
2. How would you solve \(\frac{1}{3}(6n - 9) = \frac{1}{4}(12n + 16)\)?
3. What is the solution to \(\frac{2}{5}(5n - 10) = \frac{3}{4}(8n + 16)\)?
4. Can you solve the equation \(\frac{1}{2}(2n - 8) = \frac{1}{3}(9n + 12)\)?
5. Solve the equation \(\frac{1}{6}(12n - 18) = \frac{1}{4}(16n + 24)\).

**Tip:** Always distribute fractions carefully and then combine like terms to simplify the equation.

Learn how to solve the equation 1/2(4n - 6) = 1/3(9n + 12) with a detailed step-by-step solution. This problem involves equations with fractions and the distributive property. Suitable for 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