Question

What is the value of x in the proportion StartFraction 6 x plus 1 over 7 EndFraction equals StartFraction 18 x minus 2 over 14 EndFraction?

A. 0
B. 3
C. two-thirds
D. one-fourteenth

Answer 1

C

Step-by-step explanation:

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Answer 2

The correct answer is: [C]: " two-thirds " .
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" x = "
`(2)/(3)` " ; which is: " two-thirds " .
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Step-by-step explanation:
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Given: "
`(6x + 1)/(7) = (18x-2)/(14)` " ; Solve for "x" ;
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First, multiply the first fraction by "
`(2)/(2)`" ;
{ since: "
`(2)/(2)` = 1" ; and since any value, multiplied by "1" results in that exact same value. By multiplying the first fraction by: "
`(2)/(2)`" , we can get the "denominator" in the first fraction equal to the "denominator" of the second fraction.

→
`image`" .
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Note the "distributive property of multiplication" :
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a(b + c) = ab + ac ;

a(b – c) = ab – ac .
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As such, take the "numerator" ; which is:

" 2(6x + 1) " ; and expand:

→ = (2*6x) + (2*1) = " 12x + 2 " ;

Now, we can rewrite the entire expression:
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"
`(12x+2)/(14)`" ; and we can rewrite the entire equation:
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→ "
`(12x+2)/(14)` = \frac{18x-2}{14} [/tex] " ;

Let us simplify this: " 12x + 2 = 18x – 2 " ; Solve for "x" ;
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→ 18x – 2 = 12x + 2 ;

→ Subtract "12x" from each side of the equation; and subtract "2" from each side of the equation:


→ 18x – 2 – 12x – 2 = 12x + 2 – 12x – 2 ;

to get:

→ 6x – 4 = 0 ;

Add "4" to each side of the equation:

→ 6x – 4 + 4 = 0 + 4 ;

to get:

→ 6x = 4 ;

Divide each side of the equation by "6" ;
to isolate "x" on one side of the equation; & to solve for "x" ;

→ 6x / 6 = 4 / 6 ;

→ x = 4/6 ; → "4/6" = "(4÷2)/(6÷2)" = "2/3" .

→ x = 2/3 ; → x = "
`(2)/(3)` " ; which is "two-thirds" ;

→ which is: Answer choice: [C]: " two-thirds" .
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