How do you solve $\frac{x + 5}{x - 1} = \frac{7}{6}$ $(x+5)/(x-1)=7/6$ ?

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How do you solve $\frac{x + 5}{x - 1} = \frac{7}{6}$ $(x+5)/(x-1)=7/6$ ?

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Answer 1 · 2018-04-23T19:31:24

$x = 37$ $x=37$

Explanation:

$we can use cross-multiplication to solve$ $"we can use "color(blue)"cross-multiplication ""to solve"$

$given one fraction equal to another fraction then$ $"given one fraction equal to another fraction then"$

$∙ x \frac{a}{b} = \frac{c}{d} \Rightarrow a d = b c \leftarrow cross-multiplication$ $•color(white)(x)a/b=c/drArrad=bclarrcolor(blue)"cross-multiplication"$

$\frac{x + 5}{x - 1} = \frac{7}{6}$ $(x+5)/(x-1)=7/6$

$\Rightarrow 7 (x - 1) = 6 (x + 5) \leftarrow distribute$ $rArr7(x-1)=6(x+5)larrcolor(blue)"distribute"$

$\Rightarrow 7 x - 7 = 6 x + 30$ $rArr7x-7=6x+30$

$subtract 6x from both sides$ $"subtract 6x from both sides"$

$7x-6x-7=cancel(6x)cancel(-6x)+30$

$rArrx-7=30$

$"add 7 to both sides"$

$xcancel(-7)cancel(+7)=30+7$

$color(blue)"As a check"$

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

$(37+5)/(37-1)=42/36=7/6=" right side"$

$rArrx=37" is the solution"$

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How do you solve $\frac{x + 5}{x - 1} = \frac{7}{6}$ $(x+5)/(x-1)=7/6$ ?

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How do you solve $\frac{x + 5}{x - 1} = \frac{7}{6}$ $(x+5)/(x-1)=7/6$ ?