Question

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

Answer 1

`x=-1/6`

Explanation:

Subtract `1` from both sides

`3x+1-1=1/2-1`

`3x=-1/2`

And then divide both sides by `3`

`(3x)/3=(-1/2)/3`

`-1/2` divided by `3` can also be written as `-1/2` multiplied by `1/3`

`x=(-1/2)*1/3`

`x=-1/6`

** *** OR in simpler terms *** **

Bring `1` to the other side, making sure to change its sign

`3x=1/2-1`

`3x=-1/2`

And divide both numerators by `3`

`(3x)/3=-1/(2*3)`

`x=-1/6`

Answer 2

`x = -1/6`

Explanation:

People use the term "balance the equation" to describe how to solve this. Consider 5 = 5. Which is true. Write it as (5) = (5), the brackets are only there to show what is the original 'elements' of the equation as a group. Now consider the false statement that (5) -1 = 5. To balance this we need to write (5) -1 = (5) - 1. We have applied the same process to both sides.

Solving the original equation using the same idea:
The target is to get `x` on one side of the equals sign and everything else on the other.

First isolate all the elements with `x` in them. That is "`3x`"

`(3x+1)=(1/2)`

Step1. Subtract 1 from both sides giving:
`(3x+1) -1=(1/2)-1`
`3x=-1/2`

Step2. Now we need to separate the 3 from the `x` and move it to the other side of the equals sign. This is done by changing 3 into `1` as `1 times x = x`. Dividing by three is the same as multiply by `1/3`.

Divide both sides by three

`(3x) times 1/3 = (-1/2) times 1/3`

`3/3 times x = (-1 times 1)/(2 times 3)`

thus `x = -1/6`