To solve the equation \(\frac{x+3}{2} - \frac{x}{4} = \frac{4}{3}\), we can follow these steps:

1. **Eliminate the fractions** by finding a common denominator. The common denominator for the terms involving \(x\) is 4.

2. **Multiply the entire equation by 12** (which is the least common multiple of 2, 4, and 3) to get rid of the denominators:

\[
12 \cdot \left(\frac{x+3}{2}\right) - 12 \cdot \left(\frac{x}{4}\right) = 12 \cdot \left(\frac{4}{3}\right)
\]

3. Simplifying each term:

\[
6(x + 3) - 3x = 16
\]

4. **Distribute and combine like terms**:

\[
6x + 18 - 3x = 16
\]

\[
3x + 18 = 16
\]

5. **Isolate \(x\)** by subtracting 18 from both sides:

\[
3x = 16 - 18
\]

\[
3x = -2
\]

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

\[
x = -\frac{2}{3}
\]

So, the solution is \(x = -\frac{2}{3}\).

Would you like more details on any step, or do you have any other questions?

Here are 5 related questions:

1. How can you verify the solution \(x = -\frac{2}{3}\) in the original equation?
2. What is the least common denominator (LCD) method and how is it used in solving equations?
3. How would the process change if the equation were \(\frac{2x+3}{2} - \frac{x}{4} = \frac{4}{3}\)?
4. What are the steps to solve a linear equation with variables on both sides?
5. How would you solve the equation if it were \(\frac{x+3}{2} - \frac{x+4}{4} = \frac{4}{3}\)?

**Tip:** When solving equations involving fractions, multiplying through by the least common multiple of the denominators can simplify the problem significantly.

Learn how to solve the equation (x+3)/2 - x/4 = 4/3 with a detailed step-by-step solution. This problem covers equations involving fractions and algebraic manipulation. Suitable for high school students.

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