7/2x+5 = 2/3     (7 is the numerator and 2x+5 is the denominator)

The equation you provided is:

\[
\frac{7}{2x + 5} = \frac{2}{3}
\]

To solve for \(x\), we can cross-multiply:

\[
7 \cdot 3 = (2x + 5) \cdot 2
\]

Simplifying:

\[
21 = 2(2x + 5)
\]

Now distribute the 2 on the right-hand side:

\[
21 = 4x + 10
\]

Next, subtract 10 from both sides:

\[
11 = 4x
\]

Now divide both sides by 4 to isolate \(x\):

\[
x = \frac{11}{4}
\]

Thus, \(x = \frac{11}{4}\), or \(x = 2.75\).

Would you like further details on any step? Here are some related questions:

1. How would the solution change if the right-hand side were different?
2. What if the numerator was different, say \(6\) instead of \(7\)?
3. How do you cross-multiply if there are multiple terms in the denominator?
4. Can this be solved graphically, and how would the solution look?
5. What happens when the denominator contains more complex expressions, like a quadratic?

**Tip:** When cross-multiplying, always ensure that the denominators are non-zero to avoid undefined expressions!

7/2x + 5 = 2/3 (7 is the numerator and 2x + 5 is the denominator)

Learn how to solve the rational equation 7/(2x + 5) = 2/3 by cross-multiplying and isolating the variable x. This step-by-step guide simplifies algebraic fractions and solves for x, making it suitable for students in Grades 8-10.

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