Question

How do you solve `1/3x+2=5/6`?

Answer 1

See the entire solution process below:

Explanation:

First, subtract `color(red)(2)` from each side of the equation to isolate the `x` term while keeping the equation balanced:

`1/3x + 2 = 5/6`

`1/3x + 2- color(red)(2) = 5/6 - color(red)(2)`

`1/3x + 0 = 5/6 - (6/6 xx color(red)(2))`

`1/3x = 5/6 - 12/6`

`1/3x = -7/6`

Now, multiply each side of the equation by `color(red)(3)` to solve for `x` while keeping the equation balanced:

`color(red)(3) xx 1/3x = color(red)(3) xx -7/6`

`cancel(color(red)(3)) xx 1/color(red)(cancel(color(black)(3)))x = cancel(color(red)(3)) xx -7/(color(red)(cancel(color(black)(6)))2)`

`x = -7/2`

Answer 2

`x=-7/2` or `3 1/2`

Explanation:

`1/3 x+2=5/6`

`:.x/3+2/1=5/6`

`:.(2x+12=5)/6`

`:.(2x)/6+12/6=5/6`

multiply L.H.S. and R.H.S by 6

`:.2x+12=5`

`:.2x=5-12`

`:.2x=-7`

`x=-7/2`

substitute `x=-7/2`

`:.1/3(-7/2)+2=5/6`

`:.-7/6+12/6=5/6`

`:.5/6=5/6`