Question

How do you solve `-\frac { 2x - 6} { 3} = \frac { x } { 5} + 2`?

Answer 1

x = 0

Explanation:

Multiply all the terms by 15 the least common multiple.

`15 xx -( 2x -6)/3 = 15 xx( x/5 + 2)` This gives

`-10x + 30 = 3x + 30` subtract 30 from both sides

`-10x + 30 - 30 = 3x + 30 - 30` the result is

`- 10 x = 3x` add 10x to both sides

`-10x + 10x = 3x + 10x` which equals

`0 = 13 x` divide both sides by 13

`0/13 = (13x)/13` the answer is

`0 = x`

Answer 2

Answer: `x=0`

Explanation:

Solve `-(2x-6)/3=x/5+2` for `x`.

We can start by getting rid of the fractions by multiplying everything by the least common multiple (lcm) of the denominators (`3`, `5`, and `1`), which is `15`.

So, we get:
`15(-(2x-6)/3=x/5+2)`

`-5(2x-6)=3x+30`

Simplifying, we get:
`-10x+30=3x+30`

Subtracting `30` from both sides and adding `10x` to both sides, we get:
`13x=0`

Dividing both sides by `13`, we get our answer:
`x=0`