https://file.aiquickdraw.com/mathbot/file/1725308186313l9iappss.jpg

The equation in the image is:

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

Let's solve this equation.

1. **Cross-multiply** to eliminate the fractions:
\[
2 \cdot (2x + 3) = 3 \cdot (x + 1)
\]

2. **Distribute** on both sides:
\[
4x + 6 = 3x + 3
\]

3. **Isolate** the variable \(x\). Subtract \(3x\) from both sides:
\[
4x - 3x + 6 = 3
\]
\[
x + 6 = 3
\]

4. **Solve** for \(x\) by subtracting 6 from both sides:
\[
x = 3 - 6
\]
\[
x = -3
\]

The solution is \(x = -3\).

Would you like more details on the steps or have any questions?

Here are some related questions to explore further:
1. How do you solve rational equations with more than two terms?
2. What happens if there is an extraneous solution in a rational equation?
3. Can you explain how to check if a solution is valid for the original equation?
4. How do you solve equations where the denominators are polynomials?
5. What is the importance of cross-multiplication in solving rational equations?

**Tip:** When solving rational equations, always check your solution by substituting it back into the original equation to ensure it doesn't make any denominator zero, which would invalidate the solution.

Learn how to solve the rational equation (2x + 3) / 3 = (x + 1) / 2 with a detailed step-by-step solution. This problem covers key algebraic concepts, including cross-multiplication and isolating variables. Suitable for high school students.

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