Question

How do you evaluate `\frac { 2x } { 3} - \frac { 3} { 4} =\frac { x } { 6} + \frac { 21} { 4}`?

Answer 1

`x = 12.5`

Explanation:

First things first: Put the variables on the left side of the equation and everything else on the other.

`(2x)/3 -3/4 = x/6 + 21/4 => (2x)/3 - x/6 = 21/4 + 3/4`

Then, make the whole equation to have the same denominator(doing that, we can cancel the denominator in both sides, by multiplicating them by the denominator):

`((2*2x)- x)/6= 25/4 => (3x)/6 = 25/4`

Since both sides have different denominators, we need to find the MCM(minimum commom multiple) of `6` and `4`, that is `12`. Now, we make the equation to have `12` as denominator:

`(2*3x)/12 = (3*25)/12 => (6x)/12 = 75/12 => 6x * cancel(12/12) = 75 * cancel(12/12) =>`

`6x = 75 => x = 75/6 = 12.5`