Question

What is the value of `x` in the equation `(3/4)x + 2 = (5/4)x - 6` ?

Answer 1

`x=16`

Explanation:

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

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

`8=1/2x`

`x=16`

Answer 2

`x = 16`

Explanation:

Re-arrange the equation.

Add `6` to both sides:

`(3/4)x + 2 + 6 = (5/4)x - 6 + 6`
`(3/4)x + 8 = (5/4)x`

Multiply out `(3/4)x " and " (5/4)x`:

`(3x)/4` and `(5x)/4`

Multiply it all by 4:

`3x + 8(4) = 5x`

Solve:

`3x - 3x + 32 = 5x - 3x`
`32 = 2x`

`x = 16`

Answer 3

`x=16`

Explanation:

`"collect terms in x on one side of the equation and"`
`"numeric values on the other side"`

`"subtract "3/4x" from both sides"`

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

`rArr2=1/2x-6`

`"add 6 to both sides"`

`2+6=1/2xcancel(-6)cancel(+6)`

`rArr8=1/2x`

`"multiply both sides by 2"`

`rArrx=16" is the solution"`