How do you solve 3/4 - 1/6x = 1/2 + 2x/9 for x?
Bring all terms in the variable `x` to one side of the equation and all the terms not in `x` to the other side. When a term switches sides it's sign switches. So if it is positive it becomes negative and if it is negative it becomes positive.
`-1/6x - 2/9x = 1/2 - 3/4`
Notice that the term `2/9x` switched sign from positive to negative as it was brought over to the left and the term `3/4` also switched sign from positive to negative as it was brought over to the right.
Now we gather the terms in `x` so that we have just one term:
`(-1/6 -2/9)x = 1/2 -3/4`
Now we combine the fractions
`(-3/18 - 4/18)x = 2/4 - 3/4`
Note 18 is the lowest common multiple of 6 and 9 ( = 3 x 6 and 2 x 9)
` `This gives
`-7/18x = -1/4`
To solve for ` ``x`multiply both sides by (-18/7). This gives
`x = (-1/4)(-18/7) = ((-1)(-18))/((4)(7)) = 18/28`
Simplifying this fraction (dividing both numerator and denominator by 2) we have
`x = 9/14` result (check on a calculator that both sides of the original equation = 0.643)