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## Get ready for Algebra 1

# Same thing to both sides of equations

The example of a scale where we try to achieve balance helps to explain why we do the same thing to both sides of an equation. Created by Sal Khan.

## Want to join the conversation?

- what is slope?(31 votes)
- Slope, commonly represented as "m", is the how much the line tilts on a graph. It is commonly deciphered with the form "rise over run", basically saying that you must find two points on a line, find the y difference and the x difference, and then divide the y difference by the x difference.(3 votes)

- Why exactly do we do the same thing to both sides?(2 votes)
- Its an equal sign. Both sides must be equal. Thus, whenever you do something, you also do it to the other side to keep it equal.(2 votes)

- why is x the most commonly used variable(2 votes)
- The answer that seems more likely is that many other letters are often used for particular things (t for time, D for diameter, L for length, V for volume, E for energy, etc.), but there aren't many words that start with x. So, it makes for a good general-use variable.(7 votes)

- Does algebra always have varibles, or is there always an unknown?(0 votes)
- Yes, because in algebra the basic intention using and learning the skill is to find to "unknown". But to answer your question is . . . yes.(6 votes)

- if there is a problem like x+3(squared)=12

my question is, is if the square is on the number and not the variable, does it qualify as a linear expression?(6 votes)- yes, it will always be a linear equation.

when you get that type of problem, you should try to simplify the equation, here,

x+9=12

x=12-9=3

therefore the line is x=3(8 votes)

- At1:50why is Sal removing 6 instead of 3? The third box (lower right) that is removed has a 4 in it?(0 votes)
- Ahh, yes, I guess I'm just a little dyslexic. Thought some of those were 4s. Watching it in full screen it's a little more obvious. Thanks!(5 votes)

- why do we use the dot instead of the traditional multiplication symbol in algebra?(2 votes)
- It would very confusing if you use an "x" as the multiplication sign and as a variable, therefore, we use the dot as a replacement for the "x" as a multiplication sign.(1 vote)

- What if there are variblies on both sides?(3 votes)
- If the variables are the same, then you cancel them out. For example...

3x + 6= 8x -7

You would subtract 3x. But what you do to one side you have to do to the other, leaving you with...

6= 5x -7

From there, you would have to add 7 -to cancel it out- and do the same to the other side. You SHOULD end up with...

13= 5x

It should be obvious by now -if it wasn't already- that you aren't going to get a "nice" number. But to simply it, you would have to divide 5. So your final answer should be...

13/5 = x

OR (if you wanted to simply it further...)

2.6 = x

But most math teachers will accept either answer. Although, some may say that they prefer one or the other so double check!(3 votes)

- So my equation is -2(x+5)=-6x+(x-2). I solved it to -2x-10=-2x-8. I realized that if i add 2x to both sides. my x will be 0x. Would my equation be unsolvable or do i just go with 0x?(2 votes)
- I am not sure how you got the right side of the equation as -2x - 8. If you have -6x + (x-2), the parentheses is not needed, so you have -6x + x - 2 = -5x - 2. Perhaps you left out a 4 in front of (x-2). If this is true, then you do drop the x, and end up with -10 = -8. It is not unsolvable, it is just that there is NO solution which is not quite the same, but the direction that you are aiming toward.(4 votes)

- What do we have to do if one side has more weight than the other one?(4 votes)
- When you are given a problem, the two sides are equal, so they are equally weighted. As long as you do the same thing on both sides, they remain the same weight. The only way that one side can become "more weight" on a side is if you make a math mistake, and thus the answer would not satisfy the original equation. A few common mistakes include -3x = 18, either only dividing by 3 (not -3) and dropping the negative to get x = 6 or dividing by -3 on one side and 3 on the other to get x = 6 when the answer is x = -6. A second is if you start with x + 3 = 6, and subtract 3 on one side and 6 on the other to get x = 0 instead of x = 3.(1 vote)

## Video transcript

We've got a scale here, and as
you see, the scale is balanced. And we have a
question to answer. We have this mystery
mass over here. It's a big question mark on
this blue mass right over here. And we also have
a bunch of 1-- I guess we could call
them 1-kilogram masses. So these are all each
a 1-kilogram mass. And my question to
you is, what could we do to either side of
this scale in order to figure out what
the mystery mass is? Or maybe we can't
figure it out at all. Is there something that we can
do, either removing or adding these things, so that
we can figure out what this mystery mass is? And I'll give you a couple of
seconds to think about that. Well, to figure out what
this mystery mass is, we essentially just want this
on one side of this scale. But that by itself isn't enough. We could just remove these
3, but that won't do the job, because if we just
remove these 3, then the left-hand
side of the scale is clearly going to have less
mass, and it's going to go up, and the right side
is going to go down. And that's not going to
give as much information. It's just going to tell us that
this blue thing has a lower mass than what's over here. So just removing this
won't help us much. It won't let us know that
this is equal to that. Well, what we've got to do
if we want to keep the scale balanced is we've got to
remove the same amount of mass from both sides of the scale. So if we want to remove
3 things here-- so let me try my best to
remove 3 things here. If we want to remove 3--
let me do it like this. I'll just color on it. I'll just erase it. So if we want to
remove 3 things there, if we did this by itself,
just removed these 3 things, then the two sides would not
have an equal mass anymore. This side over here
would have a lower mass. So we've got to remove
3 from both sides. So if we really
want to make sure that our scale is
balanced, we've got to remove 3 from both sides. And so if we started off
with the scales balanced and then we removed
3 from both sides, the scale will
still be balanced. And then when we do that,
we have a clearer idea of what the mass of
this object actually is. Now, when we remove
3 from both sides, the scale will
still be balanced. And we know that this mass
is equal to whatever's left over here. It's equal to 1,
2, 3, 4, 5, 6, 7. And if we're assuming
they're kilograms, we'll know that
the question mark mass is equal to 7 kilograms,
that this right over here is a 7-kilogram mass.