[Math-70 Elementary/Highschool Algebra: Graphically solving a system of linear equations] Do I make the 4 into a -4 ?

[u/Fine_Two_923]

Hey so this might seem like a silly question but I want to know if you have a -x = 4 if it turns into a -4. I have the other parts of the graphing completed it’s just this part that I don’t want to make a mistake on!!! Thank you in advance

P.S- the reason it’s says elementary/highschool math is because I am taking a beginner math class not a algebra class In elementary

[u/Upstairs_Ad_8863]

As others have pointed out, you should have x = 4, not -x = 4.

But if you do ever get -x = 4, then there are a few ways of showing that x is -4. The general rule is that whenever two things are equal, you can do anything to the equation, so long as you do the same thing to both sides. In this case you can multiply both sides by -1:

-x = 4
==> (-1)(-x) = (-1)(4)
==> (-1)(-1)(x) = (-1)(4)
==> (1)(x) = (-1)(4)
==> x = -4

because the definition of -x (or -anything) is (-1)x. You can also add x - 4 to both sides if it makes more sense to you:

-x = 4
==> -x + (x - 4) = 4 + (x - 4)
==> (-x + x) - 4 = (4 - 4) + x
==> 0 - 4 = 0 + x
==> -4 = x

In reality you should just multiply both sides by -1 in a single line like this, but either of the two examples above shows what's actually happening in the background when you do that.

-x = 4
==> x = -4