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2/7x-1/2x=3/4x+1

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tiff89 | eNotes Newbie

Posted October 21, 2013 at 5:08 PM via web

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2/7x-1/2x=3/4x+1

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aruv | High School Teacher | Valedictorian

Posted October 21, 2013 at 5:15 PM (Answer #1)

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`2/(7x)-1/(2x)=3/(4x)+1`

`2/(7x)-1/(2x)-3/(4x)=1`

`L.C.M. of (7,2,4)=28`

`(2xx4)/(7x xx4)-(1xx14)/(2x xx14)-(3xx7)/(4x xx7)=1`

`(8-14-21)/(28x)=1`

`(-27)=28x xx1`

`28x=-27`

`x=(-27)/28`

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levvy | eNoter

Posted October 30, 2013 at 7:01 PM (Answer #2)

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2/7x-1/2x=3/4x+1

first you can move 3/4x to the left side

2/7x-1/2x-3/4x=1

and let them have the same Denominator so it gives

8/28x-14/28x-21/28x=1

-27/28x=1

divide -27/28 by both sides gives

x=-28/27

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kingattaskus12 | (Level 3) Adjunct Educator

Posted November 15, 2013 at 3:22 AM (Answer #3)

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Find the LCD (least common denominator) of `2/(7x) -1/(2x) + 3/(4x) + 1`

Least common denominator: `28x`


Multiply each term in the equation by `28x` in order to remove all the denominators from the equation.

`2/(7x) * 28x - 1/(2x) * 28x = 3/(4x) * 28x + 1 *28x`


Simplify the left-hand side of the equation by canceling the common factors.

`-6 = 3/(4x) * 28x + 1 * 28x`


Simplify the equation.

`-6=28x+21 `


Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.

`28x+21=-6 `


Since `21` does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting `21` from both sides.

`28x=-21-6`


Subtract 6 from `-21` to get `-27` .

`28x=-27`


Divide each term in the equation by `28` .

`(28x)/28 = -27/28`


Simplify the equation.

`x = -27/28` 

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