How do you solve 14/(3x) = 6/(2x-5)?

Apr 2, 2015

The answer is: $x = 7$

First of all, $x \notin \left\{0 , \frac{5}{2}\right\}$

Because those values will lead a "division by zero" error, which is a great sin in maths.

Now, we can get to work.

$3 x \cdot \left(\frac{14}{3 x}\right) = 3 x \cdot \left(\frac{6}{2 x - 5}\right)$

$14 = \frac{18 x}{2 x - 5}$

$\left(2 x - 5\right) \cdot 14 = \left(2 x - 5\right) \cdot \frac{18 x}{2 x - 5}$

$28 x - 70 = 18 x$
$10 x = 70$
$x = 7$

$x$ is not $0$ or $\frac{5}{2}$ so this is a valid value.

The result is: $x = 7$