How do you solve $\frac{7}{x} = \frac{8}{5 x - 6}$ $7/x=8/(5x-6)$ ?

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How do you solve $\frac{7}{x} = \frac{8}{5 x - 6}$ $7/x=8/(5x-6)$ ?

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Answer 1 · 2016-07-09T01:46:19

The answer to that problem is $\frac{14}{9}$ $14/9$

Explanation:

In the equation, you need to remove the denominator in both sides of the given equation. To do that, you need to multiply both sides by their corresponding denominator.

$(5 x - 6) (x) (\frac{7}{x}) = (5 x - 6) (x) (\frac{8}{5 x - 6})$ $(5x-6)(x)(7/x)=(5x-6)(x)(8/(5x-6))$

Simplify

$[\frac{(5 x - 6) (x) (7)}{x}] = [\frac{(5 x - 6) (x) (8)}{5 x - 6}]$ $[[(5x-6)(x)(7)]/x]=[[(5x-6)(x)(8)]/(5x-6)]$

$7 (5 x - 6) = 8 x$ $7(5x-6)=8x$

$35 x - 42 = 8 x$ $35x-42=8x$

$35 x - 42 + 42 = 8 x + 42$ $35x-42+42=8x+42$

$35 x - 8 x = 8 x - 8 x + 42$ $35x-8x=8x-8x+42$

$27 x = 42$ $27x=42$

$\frac{27 x}{27} = \frac{42}{27}$ $(27x)/27=42/27$

$x = \frac{42}{27}$ $x=42/27$

Simplify the answer to the lowest term

$x = \frac{42}{27} \div \frac{3}{3}$ $x=42/27-:3/3$

Since both of them has the factor of 3, we will divide both the numerator and the denominator by 3.

$x = \frac{14}{9}$ $x=14/9$

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