Question

How do you solve the system of equations `-4x+3=5x-13-x`?

Answer 1

While not a system of equations, this equation can be rearranged to find that `x=2`

Explanation:

We will want to first simplify the Right Hand Side (RHS) of the equation:

`-4x+3=5x-x-13`

`-4x+3=x(5-1)-13`

`-4x+3=4x-13`

Next, we'll add/subtract values from the Left Hand Side (LHS) and the RHS to get all of the constants on one side, and all of the `x`-related terms on the other:

`cancel(-4x)+3color(red)(cancel(+4x))=4x-13color(red)(+4x)`

`3=x(4color(red)(+4))-13`

`3=8x-13`

`3color(blue)(+13)=8xcancel(-13)color(blue)(cancel(+13))`

`16=8x rArr 8x=16`

Finally, we'll divide through by `x`'s coefficient to find our solution:

`(cancel(8)x)/color(red)(cancel(8))=16/color(red)(8)`

`color(green)(x=2)`