Solve the Fraction Equation: Find X in 7/(x-4) = 5/(8x)

Q: Why can I use cross-multiplication here?

Cross-multiplication works perfectly when you have one fraction equal to another fraction, like $ \frac{7}{x-4} = \frac{5}{8x} $. This method clears both fractions in one step!

Q: How do I cross-multiply step by step?

Follow this pattern: left numerator × right denominator = right numerator × left denominator. So 7 × 8x = 5 × (x-4), which gives you 56x = 5x - 20.

Q: What if my denominator has x in it?

That's called a rational equation! Just be careful that your final answer doesn't make any denominator equal zero. Here, x ≠ 4 and x ≠ 0.

Cross-Multiplication with Rational Equations

Solve for X:

$\frac{7}{x-4}=\frac{5}{8x}$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We want to isolate the unknown X

00:07 We'll multiply by both denominators to eliminate fractions

00:20 We'll properly distribute terms, multiply by each factor

00:27 We'll arrange the equation so one side has only the unknown X

00:35 We'll isolate the unknown X

00:43 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Solve for X:

$\frac{7}{x-4}=\frac{5}{8x}$

Step-by-step solution

To solve the given equation $\frac{7}{x-4} = \frac{5}{8x}$ , we will use cross-multiplication to clear the fractions:

Cross-multiply to obtain: $7 \cdot 8x = 5 \cdot (x - 4)$ .

This simplifies to: $56x = 5x - 20$ .

Next, we need to isolate $x$ by first subtracting $5x$ from both sides:

$56x - 5x = -20$ .

This simplifies further to: $51x = -20$ .

Finally, solve for $x$ by dividing both sides by 51:

$x = \frac{-20}{51}$ .

Therefore, the solution to the equation is $x = \frac{-20}{51}$ .

Final Answer

$\frac{-20}{51}$

Key Points to Remember

Essential concepts to master this topic

Cross-Multiply: When equation has one fraction equals another fraction
Technique: $\frac{7}{x-4} = \frac{5}{8x}$ becomes 7(8x) = 5(x-4)
Check: Substitute $x = \frac{-20}{51}$ back into original equation ✓

Common Mistakes

Avoid these frequent errors

Incorrectly cross-multiplying terms
Don't cross-multiply by multiplying numerators together and denominators together = wrong setup! This creates a completely different equation. Always multiply diagonally: left numerator times right denominator equals right numerator times left denominator.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why can I use cross-multiplication here?

Cross-multiplication works perfectly when you have one fraction equal to another fraction, like $\frac{7}{x-4} = \frac{5}{8x}$ . This method clears both fractions in one step!

What if I get a negative answer?

Negative answers are completely normal in algebra! The solution $x = \frac{-20}{51}$ is correct. Just make sure to check your work by substituting back.

How do I cross-multiply step by step?

Follow this pattern: left numerator × right denominator = right numerator × left denominator. So 7 × 8x = 5 × (x-4), which gives you 56x = 5x - 20.

What if my denominator has x in it?

That's called a rational equation! Just be careful that your final answer doesn't make any denominator equal zero. Here, x ≠ 4 and x ≠ 0.

Can I simplify the fraction answer further?

Always check if you can reduce fractions! Since 20 and 51 share no common factors other than 1, $\frac{-20}{51}$ is already in simplest form.

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