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`

The equation `2/(7x)-1/(2x)=3/(4x)+1` has to be solved.

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

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

Add the coefficients of 1/x and isolate this term to one side of the equation.

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

`(1/x)*(-27/28) = 1`

`1/x = 1*(-28/27)`

`x = -27/28`

The required solution of the equation is `x = -27/28`

QUESTION:-

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

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

SOLUTION:-

Bring all of the digits except 1 on LHS, since 1 does not contain any x value;

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

Find the LCD (Lowest Common Denominator). Here the LCD of 7,2 and 4 is 28, hence;

`2/(7x)*(4/4)-1/(2x)*(14/14)-3/(4x)*(7/7)=1`

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

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

`-27/(28x)=1`

`-27=28x`

`x=-27/28`

Hence the answer is x = -27/28

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

To simplify this we first need to take the least common denominator, also we need to shift 3/4x to LHS,

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

`28 is the LCD`

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

`-27/(28x) = 1`

`-27/(28x) * 28x = 1 * 28x`

`-27 = 28x`

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

`-27/28 = x`

`x = -27/28 Answer.`

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

`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`