Question

How do you solve for x: `12/x+3/4=3/2`?

Answer 1

`x=16`

Explanation:

Solution 1.

By inspection of the equation `12/x+3/4=3/2`

We know that `3/4+3/4=3/2`, and `12/16=3/4`.
Therefore, `x=16`

Solution 2.

By Algebraic procedure

`12/x+3/4=3/2`

Multiply both sides of the equation by `x`

`x(12/x+3/4)=(3/2)x`

`12+(3x)/4=(3x)/2`

`12=(3x)/2-(3x)/4`

`12=(6x-3x)/4`

`12=(3x)/4`

`x=(12*4)/3`

`x=16`

God bless....I hope the explanation is useful.

Answer 2

`x=16`

Explanation:

In an equation which has fractions, we can get rid of the denominators by multiplying all the terms by the LCM of the denominators.

`12/x+3/4=3/2" LCM " =color(magenta)(4x)`

`(color(magenta)(4x)xx12)/x+(color(magenta)(4x)xx3)/4=(3xxcolor(magenta)(4x))/2`

`(color(magenta)(4cancelx)xx12)/cancelx+(color(magenta)(cancel4x)xx3)/cancel4=(3xxcolor(magenta)(cancel4^2x))/cancel2color(magenta)`

`48 +3x = 6x`

`48 = 3x`
`x = 16`