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The correct answer is: [C]: " two-thirds <span>" .
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" x = "
" ; which is: " two-thirds " .
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Explanation:
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Given: "
" ; Solve for "x" ;
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First, multiply the first fraction by "
" ;
{ since: " = 1" ; and since any value, multiplied by "1" results in that exact same value. By multiplying the first fraction by: "" , we can get the "denominator" in the first fraction equal to the "denominator" of the second fraction.
→
" .
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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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"
" ; and we can rewrite the entire equation:
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→ " = \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 = " " ; which is "two-thirds" ;
→ which is: Answer choice: [C]: "<span> two-thirds</span><span>" .
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</span>____________________________________________________
" x = "
____________________________________________________
Explanation:
____________________________________________________
Given: "
____________________________________________________
First, multiply the first fraction by "
{ since: "
→
___________________________________________________________
Note the "distributive property of multiplication" :
_______________________________________________________
a(b + c) = ab + ac ;
a(b – c) = ab – ac .
_______________________________________________________
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:
________________________________________
"
________________________________________
→ "
Let us simplify this: " 12x + 2 = 18x – 2 " ; Solve for "x" ;
_____________________________________________________
→ 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 = "
→ which is: Answer choice: [C]: "<span> two-thirds</span><span>" .
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