4 x ​

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.