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### Course: Grade 6 (Virginia)>Unit 8

Lesson 2: One-step equations intuition

# 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?

• Does algebra always have varibles, or is there always an unknown?
• When we use "both sides" that means both sides of what?
• He means both sides of equation. Left of = sign, and right of = sign. Hope it helps :)
• Why exactly do we do the same thing to both sides?
• It keeps it equal. So, for example, if I had 7=7, and I wanted to add 2 to the left side, I'd have to add 2 to the right side to make both sides equal again: 7+2=7+2 or 9=9.

You can kind of think of it as "both sides are essentially saying the exact same thing." if we say x+3=9, we're saying x+3 is the exact same thing as 9. "x+3" literally means "9." So, if we were to subtract 3 from our "x+3," we'll have to do the exact same thing to our "9" (subtract 3) to make them stay the same thing.
• what is slope?
• 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.
• why is x the most commonly used variable
• 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.
• 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?
• 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
• At why is Sal removing 6 instead of 3? The third box (lower right) that is removed has a 4 in it?
• 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!
• why do we use the dot instead of the traditional multiplication symbol in algebra?
• It would be confusing if you used x as a variable and a multiplication sign, so there's a dot to replace the traditional multiplication symbol.
• here is a proof that this law does not work.... i think....
let a=b
then
a x b = b x b
then ab=b^2
subtract a^2 from either side:
ab - a^2 = b^2 -a^2
or, a(b - a) = (b + a)(b - a)
now divide both sides by b - a
then,
a = b + a
but this contradicts the fact that a = b
?
this was told by my friend and this racked my brains and he does not tell me the reason. anyone who explains this will be greatly appreciated.
• You are wrong. If a = b then a and b can’t be different numbers. This is a wrong statement
• What if there are variblies on both sides?
• 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!