Two equations that have the same solution are called equivalent equations e.g. 5 +3 = 2 + 6. And this as we learned in a previous section is shown by the equality sign =. An inverse operation are two operations that undo each other e.g. addition and subtraction or multiplication and division. You can perform the same inverse operation on each side of an equivalent equation without changing the equality.
5+3−2=6+2−2
This gives us a couple of properties that hold true for all equations.
The addition property of equality tells us that adding the same number to each side of an equation gives us an equivalent equation
ifa−b=c,thena−b+b=c+b,ora=c+b
The same goes with the subtraction property of equality.
ifa+b=c,thena+b−b=c−b,ora=c−b
As well as it goes for the multiplication property of equality. If you multiply each side of an equation with the same nonzero number you produce an equivalent equation.
ifab=c,andb≠0,thenab⋅b=c⋅b,ora=cb
And naturally this goes for the division property of equality as well. You can divide each side of an equation with the same nonzero number to produce an equivalent equation
ifa⋅b=c,andb≠0,thena⋅bb=cb,ora=cb
This gives us a way to change an equation to our own liking. Anything is acceptable as long as you do the same thing on both sides.
so pretty much what I'm tryna say it x=4
sorry for being so extra-
