Question

If 1/2x+1/2(1/2x+1/2(1/2x+1/2(1/2x+1/2...=y what does x equal?
A.

2/4
B.

1/2
C.

1/4
D.

1

Answer 1

C

Answer 2

12 x+12 (12 x+12 (12 x+12 (12 x+12 )))


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$\mathrm{Multiply\:}x\frac{1}{2}\::\quad\frac{x}{2}$Multiply x12 : x2
$=\frac{x}{2}+\frac{1}{2}\left(x\frac{1}{2}+\frac{1}{2}\left(\frac{1}{2}\left(\frac{1}{2}+x\frac{1}{2}\right)+x\frac{1}{2}\right)\right)$=x2 +12 (x12 +12 (12 (12 +x12 )+x12 ))


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$\mathrm{Multiply\:}\frac{1}{2}\left(x\frac{1}{2}+\frac{1}{2}\left(x\frac{1}{2}+\frac{1}{2}\left(x\frac{1}{2}+\frac{1}{2}\right)\right)\right)\::\quad\frac{\frac{x}{2}+\frac{\frac{x}{2}+\frac{\frac{x}{2}+\frac{1}{2}}{2}}{2}}{2}$Multiply 12 (x12 +12 (x12 +12 (x12 +12 ))) : x2 +x2 +x2 +12 2 2 2
$=\frac{x}{2}+\frac{\frac{x}{2}+\frac{\frac{x}{2}+\frac{\frac{x}{2}+\frac{1}{2}}{2}}{2}}{2}$=x2 +x2 +x2 +x2 +12 2 2 2



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$\frac{\frac{x}{2}+\frac{\frac{x}{2}+\frac{\frac{1}{2}+\frac{x}{2}}{2}}{2}}{2}:\quad\frac{7x+1}{16}$x2 +x2 +12 +x2 2 2 2 : 7x+116
$=\frac{x}{2}+\frac{7x+1}{16}$=x2 +7x+116


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$\mathrm{Find\:the\:LCD\:for}\:\frac{x}{2}+\frac{7x+1}{16}:\quad16$Find the LCD for x2 +7x+116 : 16


$\mathrm{Adjust\:Fractions\:based\:on\:the\:LCD}$Adjust Fractions based on the LCD

$=\frac{x\cdot\:8}{16}+\frac{7x+1}{16}$=x· 816 +7x+116


$\mathrm{Since\:the\:denominators\:are\:equal,\:combine\:the\:fractions}:\quad\frac{a}{c}\pm\frac{b}{c}=\frac{a\pm\:b}{c}$Since the denominators are equal, combine the fractions: ac ±bc =a± bc
$=\frac{8x+7x+1}{16}$=8x+7x+116


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$\mathrm{Simplify}\:8x+7x+1:\quad15x+1$Simplify 8x+7x+1: 15x+1


$=\frac{15x+1}{16}$=15x+116

Answer 3

Thank guys