Question

How do you solve `\frac { 10x } { 11} = \frac { x } { 3} + 19`?

Answer 1

`x=33`

Explanation:

`(10x)/11=x/3+19`

`:.(10x)/11=x/3+19/1`

`:.(30x=11x+627)/33`

`:.(30x)/33=(11x)/33+627/33`

multiply L.H.S. and R.H.S. by `33/1`

`:.30x=11x+627`

`:.30x-11x=627`

`:.19x=627`

`:.x=627/19`

`:.x=33`

Answer 2

`x=33`

Explanation:

To eliminate the fractions in the equation, multiply ALL terms on both sides of the equation by the `color(blue)"lowest common multiple"` (LCM ) of the denominators 11 and 3

the LCM of 11 and 3 is 33

`rArr(cancel(33)^3xx(10x)/cancel(11)^1)=(cancel(33)^(11)xxx/cancel(3)^1)+(33xx19)`

`rArr30x=11x+627`

subtract 11x from both sides.

`30x-11x=cancel(11x)cancel(-11x)+627`

`rArr19x=627`

To solve for x, divide both sides by 19

`(cancel(19) x)/cancel(19)=627/19`

`rArrx=33`

`color(blue)"As a check"`

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

`"left side "=(10xx33)/11=330/11=30`

`"right side "=33/3+19=11+19=30`

`rArrx=33" is the solution"`