The given equation is:

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

Let's solve for \(x\).

### Step 1: Cross-multiply
We can eliminate the denominators by cross-multiplying:

\[
4(2x + 3) = 5x
\]

### Step 2: Distribute the 4 on the left-hand side
\[
8x + 12 = 5x
\]

### Step 3: Move all terms involving \(x\) to one side
Subtract \(5x\) from both sides:

\[
8x - 5x + 12 = 0
\]
\[
3x + 12 = 0
\]

### Step 4: Isolate \(x\)
Subtract 12 from both sides:

\[
3x = -12
\]

Now, divide by 3:

\[
x = -4
\]

Thus, the solution is \(x = -4\).

Do you have any questions or want more details?

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Here are 5 related questions:
1. How do you check if \(x = -4\) satisfies the original equation?
2. What happens if \(x = 0\) in this equation?
3. Can you find similar equations that involve quadratic expressions?
4. What would change if the equation had a square root?
5. How can you solve rational equations with different denominators?

**Tip:** Always check if your solution introduces any restrictions or extraneous solutions, especially when dealing with fractions.

Learn how to solve the rational equation 4/x = 5/(2x + 3) through cross-multiplication and algebraic manipulation. This step-by-step solution covers essential algebraic techniques and is ideal for students in Grades 9-10.

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