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Lesson 2: One-step equations intuition

# One-step equations intuition

In this math lesson, we learn how to solve a balance scale problem with unknown mass. We represent the problem using an algebraic equation, 3x = 9, where x is the unknown mass. By dividing both sides by 3, we find that x = 3, meaning each object has a mass of 3 kilograms. Created by Sal Khan.

## Want to join the conversation?

• To simplify, could sal just do the square root of 9, which would be 3?
• In this case, the answer is no. If you do something to one side, you have to do it to the other, and there is no way to take the square root of 3x. This is what I mean:

sqrt 3x = sqrt 9.

And taking the sqrt of 3x does not help you in solving for x.

Hope that helped!
• When I see 3x=9 I think of the lesson before solving equations/testing solutions. I naturally did 3(3)=9 because we were taught how to make sure one side is equal to the other. Can you explain why doing 3(3)=9 is wrong and why we would do (1/3)3x = 9(1/3) =3. or should I always do the opposite, if 3(x)=9i would do 3/3=0 and 9/3=3
• Well, the first method I could understand since you probably memorised that 3 times 3 is 9. But when we get to some huge numbers, we need more concrete calculations. This is where the 2nd method comes in. We isolate the variable.

• are the blue boxes supposed too be variables ?
• Yes. There are three blue boxes with x's on them which basically means 3x.
• is X cubed same as 3x or is it the third power?
• x cubed is x to the third power, or x * x * x. Often written x³
It is NOT the same as 3x
• Wait, can x be anything else? Such as y or ! @ # etc etc ...
• yes x can stand for anything or any number good luck
• why write the divide 1/3rd instead of just putting a fractional dividing line under 3x?
• They achieve the same results. Multiplying by 1/3 and dividing by 3 are the same. So, pick which one you are comfortable with and use it.
• Whilst I understand where it came from, Sal should have explained where the third came from. It coming from factors is not obvious to all.
• This should go into the tips and thanks!
• could we divde then by them for exeample 9/3 = 3