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### Course: 6th grade (Illustrative Mathematics)>Unit 6

Lesson 3: Lesson 3: Staying in balance

# Same thing to both sides of equations

In this fun math problem, we have a balanced scale with a mystery mass on one side and several 1-kilogram masses on the other. To find the mystery mass, we remove the same number of 1-kilogram masses from both sides, keeping the scale balanced. Then, we can easily determine the mystery mass's weight. 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?
• So it would become equal.
• 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
• 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.
• 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!