Question

How do you solve `(3x-1)/3-(x-3)/15=(2x+3)/2`?

Answer 1

Isolate the first part:

`(3x - 1)/3 - (x-3)/15`

Get the denominator (both bottom numbers) equal buy multiplying the tops and bottoms. 15 is a common multiple of 3 and 15 so multiply the first fraction by 5 and the second by 1.

`(5(3x - 1))/15 - (x-3)/15` Now expand and subtract the two

`(15x -5 )/15 - (x - 3)/15`

`(15x - 5 - x + 3)/15 = (14x - 2)/15`

Put it back in the whole equation:

`(14x - 2)/15 = (2x + 3)/2`

Both have a common multiple of 30, so, multiply the first part by 2 and the second by 15.

`(2(14x - 2))/30 = (15(2x + 3))/30`

`(28x - 4)/30 = (30x + 45)/30`

`28x -4 = 30x + 45`
`-2x = 49`

`x = -24.5`