How do you solve $\frac{14}{3 x} = \frac{6}{2 x - 5}$ $14/(3x) = 6/(2x-5)$ ?

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Answer 1 · 2015-04-02T18:35:46

The answer is: $x = 7$ $x=7$

First of all, $x \notin {0, \frac{5}{2}}$ $x !in {0, 5/2}$

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

Now, we can get to work.

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

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

$(2 x - 5) \cdot 14 = (2 x - 5) \cdot \frac{18 x}{2 x - 5}$ $(2x-5) * 14 =(2x-5) * (18x)/(2x-5)$

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

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

The result is: $x = 7$ $x=7$

How do you solve 14/(3x) = 6/(2x-5)143x=62x−514/(3x) = 6/(2x-5)?