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

Question

Solve for X:

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

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

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

$\frac{-20}{51}$