Question

How do you solve `\frac { 9x } { 2} + \frac { 3} { 4} = - \frac { 33} { 4}`?

Answer 1

`x=-2`

Explanation:

To eliminate the fractions in the equation multiply ALL terms on both sides by the `color(blue)"lowest common multiple"` ( LCM) of 2 and 4, the denominators of the fractions.

The LCM of 2 and 4 is 4

`(cancel(4)^2 xx(9x)/cancel(2)^1)+(cancel(4)^1 xx3/cancel(4)^1)=(cancel(4)^1xx-33/cancel(4)^1)`

`rArr18x+3=-33larrcolor(red)" no fractions"`

subtract 3 from both sides.

`18xcancel(+3)cancel(-3)=-33-3`

`rArr18x=-36`

divide both sides by 18

`(cancel(18) x)/cancel(18)=(-36)/18`

`rArrx=-2`

`color(blue)"As a check"`

Substitute this value into the left side of the equation and if equal to the right side then it is the solution.

`"left side "=((9xx-2))/2+3/4=-9+3/4=-8 1/4=-33/4`

`rArrx=-2" is the solution"`