Question

2x + 5=11... i suck

Answer 1

x=3

Answer 2

how?!

Answer 3

i knoe you gotta subtract the 2 or something from either side but im lost after that

Answer 4

Hey, I'll explain for you.

So, you want to know what x is, so you have to make your equation look like:

x = "something"

Putting the equation into this form is called "isolating x".

Okay, so to isolate x, we need x all by itself, but right now its being multiplied by a number, and another number is being subtracted from that!

***HERE IS A REALLY IMPORTANT PART***
In math, if we do the same thing to both sides of the "=" sign, then we haven't really changed the equation.

For example, we can say:
3 = 3
Now, we can do the same thing to both sides.. say multiply by 2.
3*2 = 3*2 ---> 6 = 6

We did the same thing to both sides, and our equality is still true, 3=3 is true and 6=6 is true.

If you have a variable in the equation, this principle does not change. If we have the equation:
2x = 3
We can multiply both sides by 2, like before, and get:
2x * 2 = 3*2 ---> 4x = 6


Now, we can use this to "isolate x"

Our equation is:
2x + 5 = 11

We need to do something to both sides that will help us to get x by itself. The '+5' is kind of annoying, so lets subtract 5 from both sides.
2x + 5 - 5 = 11 - 5 ---> 2x = 6

Since we had + 5 and - 5 on the same side, they cancel. (In other words, 5 is being added to 2x, and 5 is being subtracted from it, so there is no change.)

Now, we have 2x on one side, meaning x is being multiplied by 2. If you multiply something by a number, and then divide by the same number, you get the original "something". To prove this to yourself, take a number, say 4. multiplying by 2 gives us 8. Then if we divide 8 by 2, we get 4 (our original number.

So we have 2x = 6 at this point. We can divide both sides by 2:
\[\frac{2x}{2} = \frac{6}{2}\]

Which gives us:

\[x = 3\]