Question

3/2x - 2/3x=2

I need the answer for this, please. And with steps on how you got the answer because I dont understand it. Find the value for x

Answer 1

`x = 0 \: or \: 4.17 * {10}^( - 1)` ( 5 /12 )

`(3)/(2x) - (2)/(3x) = 2`

multiplying the denominators to get the L.C.M since there is no common factor.

`2x * 3x = 6 {x}^(2)`

as the L.C .M

so now the general equation becomes

`\frac{ (3)/(2x) - (2)/(3x) }{6 {x}^(2) } = 2`

`\frac{9x - 4x}{6 {x}^(2) } = 2`

`5x = 6 {x}^(2) * 2`

`5x = 12 {x}^(2)`

`12 {x}^(2) - 5x = 0`

factorizing x

`x(12x - 5) = 0`

`x = 0`

`12x - 5 = 0`

`12x = 5`

`x = (5)/(12)`

`x = 0.416`

`x = 4.17 * {10}^( - 1)`