Question

How do you solve `\frac { 3x } { 2} - 3= \frac { x } { 3} + \frac { 1} { 2}`?

Answer 1

`x=23/9` OR `x=2.bar5`

Explanation:

You first want to get the terms that have an `x` onto one side, and the terms without one onto the other. This can be done by subtracting `-x/3` on both sides, and by adding `3` onto both sides.
Then you get
`(3x)/2-x/3=3+1/2`

Find common denominators for the left hand side (which is 6) and change the right hand side to a mixed number:
`(9x)/6-2/6=7/2`

The left hand side can now be written as
`(9x-2)/6=7/2`

Multiply both sides by 6:
`9x-2=42/2`

Simplify the right hand side:
`9x-2=21`

Add 2 to both sides:
`9x=23`

Divide both sides by 9:
`x=23/9`