`3/4 - 1/6x =1/2 +(2x)/9`

Multiply -`1/6` by x to get `-x/6`

`3/4 - x/6 = 1/2 +(2x)/9`

Let's move all the variables to the left hand side of the equation by subtracting `(2x)/9` from both sides.

`3/4 - x/6 - (2x)/9 = 1/2`

In order to combine fractions, the denominators must be equal. This can be done by finding the least common denominator (LCD). Here the LCD is 18.

`((-2x)/9 * 2/2) - (x/6 * 3/3) + 3/4 =1/2`

`(-4x)/18 - (3x)/18 +3/4 = 1/2`

`(-7x)/18 +3/4 =1/2`

Next get x alone on one side of the equation by subtracting 3/4 from both sides.

`-(7x)/18 = -3/4 +1/2`

`-(7x)/18 = -1/4`

Multiply each term by 18.

`-(7x)/18 *18 = -1/4 *18`

Cancel the common factors.

`-7x = -1/4 *18`

`-7x = -9/2`

Divide each term in the equation by -7.

`(-7x)/-7 = (-9/2)/-7`

`(-7x)/-7=-9/2 * -1/7`

Simplify.

`x=-9/2 * -1/7`

**x=9/14**

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