Question #82ba7

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Question #82ba7

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Answer 1 · 2017-04-14T20:32:34

$x = - 4$ $x=-4$

Explanation:

Use the method of $cross- multiplying$ $color(blue)"cross- multiplying"$

$Given \frac{a}{b} = \frac{c}{d} then$ $"Given " a/b=c/d" then"$

$∙ \times a d = b c$ $•color(white)(xx) ad=bc$

$\Rightarrow \frac{3}{x + 1} = \frac{5}{x - 1}$ $rArr3/(x+1)=5/(x-1)$

$\Rightarrow 5 (x + 1) = 3 (x - 1)$ $rArr5(x+1)=3(x-1)$

distributing gives.

$5 x + 5 = 3 x - 3$ $5x+5=3x-3$

$subtract 3x from both sides$ $"subtract 3x from both sides"$

$5x-3x+5=cancel(3x)cancel(-3x)-3$

$rArr2x+5=-3$

$"subtract 5 from both sides."$

$2xcancel(+5)cancel(-5)=-3-5$

$rArr2x=-8$

$"divide both sides by 2"$

$(cancel(2) x)/cancel(2)=(-8)/2$

$rArrx=-4$

$color(blue)"As a check"$

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

$"left side " =3/(-4+1)=3/(-3)=-1$

$"right side " =5/(-4-1)=5/(-5)=-1$

$rArrx=-4" is the solution"$

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Question #82ba7

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