Question

How do you simplify `\frac{1}{3}x+2=\frac{1}{2}x-1`?

Answer 1

Multiply by 6

`2x+12=3x-6`

Subtract `2x`

`12=x-6`

Add6

`x=18`

Answer 2

`x=18`

Explanation:

Given: `1/3x+2=1/2x-1`.

Subtract `2` from both sides.

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

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

Multiply both sides by the greatest common factor `(bb(GCF))` of the denominators, which is `2*3=6`.

`6(1/3x)=6(1/2x-3)`

`2x=3x-18`

Subtract `3x` from both sides.

`2x-3x=-18`

`-x=-18`

Multiplying both sides by `-1` yields:

`:.x=18`

Answer 3

`x=18`

Explanation:

We can get rid of the fractions by multiplying by the LCM of the denominators, which happens to be `6`.

We now have

`2x+12=3x-6`

Let's subtract `12` from both sides to get

`2x=3x-18`

Next, we can subtract `3x` from both sides. We now have

`-x=-18`

Lastly, we can divide both sides by `-1` to get

`x=18`

Hope this helps!