https://file.aiquickdraw.com/mathbot/file/17270525843651bkjuoua.jpg

The equation presented in the image is:

\[
\frac{5}{2} = \frac{4x + 21}{x - 3}
\]

### To solve this equation:
1. **Cross-multiply** to eliminate the fractions:
   \[
   5(x - 3) = 2(4x + 21)
   \]
   
2. **Expand both sides**:
   \[
   5x - 15 = 8x + 42
   \]
   
3. **Move all terms involving \(x\) to one side and constants to the other side**:
   \[
   5x - 8x = 42 + 15
   \]
   \[
   -3x = 57
   \]

4. **Solve for \(x\)**:
   \[
   x = \frac{57}{-3} = -19
   \]

### Solution:
\[
x = -19
\]

Would you like further details or have any additional questions?

Here are 5 related questions you might consider:
1. How do you check if the solution satisfies the original equation?
2. What would happen if there was no solution to this equation?
3. Can you solve a similar equation with different coefficients?
4. How would you solve the equation if it had a quadratic term?
5. How does cross-multiplication work with inequalities?

**Tip**: Always check for restrictions in the denominator (e.g., \(x \neq 3\) in this case to avoid division by zero).

Solve the equation 5/2 = (4x + 21)/(x - 3)

Learn how to solve the linear equation 5/2 = (4x + 21)/(x - 3) using cross-multiplication. This problem covers key algebraic concepts such as cross-multiplication and solving for x. Suitable for students in Grades 9-11.

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