Question

How do you simplify `(x-c)-(2x-4c)`?

Answer 1

`(x-c)-(2x-4c)=-x+3c`

Explanation:

From the given `(x-c)-(2x-4c)=(x-c-2x+4c)=x-2x-c+4c`
`=-x+3c`

God bless....I hope the explanation is useful.

Answer 2

`(x-c)-(2x-4c)" "->" "3c-x`

Explanation:

Consider `-(2x-4c)`

This is stating that everything inside the bracket is to be multiplied by `(-1)`

Technically you could write

`color(blue)((-1))color(brown)(xx(2x-4c))` but it is not considered to be good mathematical practice.

So we have `color(brown)(-(2x-4c)" " ->" " color(blue)((-1)xx)2x -color(blue)((-1)xx)4c)`

Notice we have two minuses together in the multiplication
`color(brown)(-color(blue)((-1)xx)4c)`. This gives us a positive. So the whole bracketed part of `-(2x-4c)` becomes: `-2x+4c`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So by removing the brackets we have:

`x-c-2x+4c`

Grouping like terms

`4c-c+x-2x`

Counting up all the `c's` we end up with `+3c`
Counting all the `x's` we end up with `-x`

Putting it all together

`(x-c)-(2x-4c)" "->" "3c-x`