How do you solve $5 - \frac{2}{x - 6} = \frac{10 - 2 x}{x - 6}$ $5-2/(x-6) = (10-2x)/(x-6)$ ?

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Answer 1 · 2017-05-29T06:31:13

no solution

Let's give everything the same denominator. Fortunately, two of the three components already share the same denominator $(x - 6)$ $(x-6)$ .

If we multiply $5$ $5$ by $\frac{x - 6}{x - 6}$ $(x-6)/(x-6)$ , all the components will be "combinable":

$\frac{5 x - 30}{x - 6} - \frac{2}{x - 6} = \frac{10 - 2 x}{x - 6}$ $(5x-30)/(x-6) - 2/(x-6) = (10-2x)/(x-6)$

Combine like-terms

$\frac{(5 x - 30) - (2)}{x - 6} = \frac{10 - 2 x}{x - 6}$ $((5x-30)-(2))/(x-6) = (10-2x)/(x-6)$

Multiply by ( $x - 6$ $x-6$ ) on both sides

$5 x - 30 - 2 = 10 - 2 x$ $5x-30-2 = 10-2x$

Simplify

$5 x - 32 = 10 - 2 x$ $5x-32=10-2x$

Add 2x to both sides

$7 x - 32 = 10$ $7x-32=10$

Add $32$ $32$ to both sides

$7 x = 42$ $7x=42$

Divide by $7$ $7$ on both sides

$x = 6$ $x=6$

Just to check our work, let's solve the equation, replacing $x$ $x$ with $6$ $6$ :

$5 - \frac{2}{6 - 6} = \frac{10 - 2 \times 6}{6 - 6}$ $5- 2/(6-6) = (10-2xx6)/(6-6)$

$5 - \frac{2}{0} = \frac{- 2}{0}$ $5-2/0=(-2)/0$

Uh oh! We're dividing by ZERO! that's illegal, so there are no solutions.

How do you solve 5-2/(x-6) = (10-2x)/(x-6)5−2x−6=10−2xx−65-2/(x-6) = (10-2x)/(x-6)?