We are given the equation:

\[
\frac{1}{5}(n + 3) = \frac{1}{4}(n + 2)
\]

### Step 1: Eliminate the fractions
To eliminate the fractions, multiply both sides by the least common denominator (LCD) of 5 and 4, which is 20.

\[
20 \times \left(\frac{1}{5}(n + 3)\right) = 20 \times \left(\frac{1}{4}(n + 2)\right)
\]

This simplifies to:

\[
4(n + 3) = 5(n + 2)
\]

### Step 2: Expand both sides
Now, distribute the constants on both sides:

\[
4n + 12 = 5n + 10
\]

### Step 3: Solve for \(n\)
To isolate \(n\), move the terms involving \(n\) to one side and the constants to the other side. Subtract \(4n\) from both sides:

\[
12 = n + 10
\]

Then subtract 10 from both sides:

\[
2 = n
\]

Thus, the solution is:

\[
n = 2
\]

Would you like a detailed explanation of any part? Here are some related problems to further practice:

1. Solve \(\frac{2}{3}(x + 5) = \frac{3}{4}(x + 1)\).
2. Solve \( \frac{1}{2}(m + 7) = \frac{2}{5}(m + 4) \).
3. Solve \( 3(n - 2) = \frac{1}{2}(n + 8) \).
4. Solve \(\frac{1}{6}(2n + 9) = \frac{2}{3}(n + 3)\).
5. Solve \(4(n + 5) = \frac{5}{3}(n + 8)\).

**Tip**: When solving equations with fractions, multiplying by the least common denominator (LCD) is an efficient way to eliminate the fractions.

Learn how to solve the linear equation with fractions: 1/5(n + 3) = 1/4(n + 2). This step-by-step solution covers key algebraic concepts like eliminating fractions using the least common denominator and simplifying linear equations. Suitable for students in Grades 6-8.

Math Problem Statement

Solve:
1 5 ( n + 3 )

Solution

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