https://file.aiquickdraw.com/mathbot/file/17254594266752x5gxu2b.jpg

The equation in the image is:

\[
\frac{1}{2x - 3} = \frac{3}{4x + 2}
\]

To solve for \( x \), follow these steps:

1. **Cross-multiply** to eliminate the fractions:

\[
1 \cdot (4x + 2) = 3 \cdot (2x - 3)
\]

2. **Distribute** on both sides:

\[
4x + 2 = 6x - 9
\]

3. **Move all terms involving \( x \)** to one side and constant terms to the other:

\[
4x - 6x = -9 - 2
\]

4. Simplify the equation:

\[
-2x = -11
\]

5. **Solve for \( x \)**:

\[
x = \frac{-11}{-2} = \frac{11}{2} = 5.5
\]

So, the solution is \( x = 5.5 \).

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

Here are 5 related questions to expand your understanding:
1. How would the solution change if the equation were \(\frac{1}{2x - 3} = \frac{2}{4x + 2}\)?
2. Can you solve a similar equation with different coefficients, such as \(\frac{2}{3x - 1} = \frac{4}{5x + 7}\)?
3. What happens if both sides of the equation have additional constants, like \(\frac{1 + 3}{2x - 3} = \frac{3 + 1}{4x + 2}\)?
4. How would you solve an equation where the denominators involve quadratic expressions, like \(\frac{1}{x^2 - 4} = \frac{3}{x^2 + 2x}\)?
5. What is the geometric interpretation of the equation \(\frac{1}{2x - 3} = \frac{3}{4x + 2}\)?

**Tip:** When solving equations involving fractions, cross-multiplication is a powerful tool to eliminate the fractions and simplify the equation.

Solve the equation 1/(2x - 3) = 3/(4x + 2).

Learn how to solve the linear equation with fractions 1/(2x - 3) = 3/(4x + 2) using cross-multiplication. This step-by-step solution is suitable for students in Grades 9-10, covering key algebraic concepts.

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