Question

How do I solve for x?

Answer 1

Solving:

`(3+4x)/(2) + (5-x)/(3) = (29)/(6)`
Make the Least Common Multiple (2,3,6)

`2,3,6\:|2`

`1,3,3\:|3`

`1,1,1\:|\underline{2*3=6}`


Replace denominators and resolve:

`(3+4x)/(2) + (5-x)/(3) = (29)/(6)`

`(3(3+4x))/(6) + (2(5-x))/(6) = (29)/(6)`
Cancel the dominators

`(3(3+4x))/(\diagup\!\!\!\!6) + (2(5-x))/(\diagup\!\!\!\!6) = (29)/(\diagup\!\!\!\!6)`

`3(3+4x) + 2(5-x) = 29`

`9 + 12x + 10 - 2x = 29`

`12x - 2x = 29 - 9 - 10`

`10x = 20 - 10`

`10x = 10`

`x = (10)/(10)`

`\boxed{\boxed{x = 1}}\end{array}}\qquad\quad\checkmark`