Question

How do you solve `-4x = - x + 3`?

Answer 1

`x=-1`

Explanation:

In algebra, we have an equation sign - it's like a balance. The thing on the one side is exactly equal to the thing on the other side. And we can change what is on the one side but we must always make sure to do the same thing to the other side - otherwise the scales will no longer be in balance.

In the question, we have an unknown quantity, x, multiplied by -4. On the other side, we have the same unknown quantity, multiplied by -1 and to which we are adding 3.

What is the value of the unknown quantity x?

We can figure this out by being clever in what we do to both sides of the equation. First we want to have the unknown quantity only on one side. We can do this by adding x to both sides - that will remove the -x on the right:

`-4x=-x+3`

`-4xcolor(red)(+x)=-xcolor(red)(+x)+3`

`-3x=3`

And now we can divide both sides by -3 to see what x is:

`(-3x)/color(red)(-3)=3/(color(red)(-3))`

`x=-1`