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## Algebra (all content)

### Course: Algebra (all content) > Unit 2

Lesson 7: Linear equations with variables on both sides- Why we do the same thing to both sides: Variable on both sides
- Intro to equations with variables on both sides
- Equations with variables on both sides: 20-7x=6x-6
- Equations with variables on both sides
- Equation with variables on both sides: fractions
- Equations with variables on both sides: decimals & fractions
- Equation with the variable in the denominator
- Figuring out missing algebraic step

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# Figuring out missing algebraic step

Created by Sal Khan.

## Want to join the conversation?

- I find it interesting that the equation:

x/3+2=7

When started by multiplying both sides by three

and then subtracting both sides by 2 will give a result of:

X=19

However, when solving it by subtracting both sides by two and then multiplying both sides by three the result will be X=15.

I will always keep this in mind when solving equations from now on.(3 votes) - Why do you distribute the 3 to only one side?(2 votes)
- you don't . you have to do it to both sides(2 votes)

- Which number is <197 and >97?(2 votes)
- Any number that is less than 197 and greater than 97. For example 100, 148, 179, etc. It can also be a fraction or decimal such as 97.0000001, 196.9999, 105.5, 105/1000, etc.(0 votes)

- I'm not understanding WHY he's distributing the 3...Anyone mind explaining this?(1 vote)
- That's just how Steven chose to solve the problem, probably because it's easier to visualize the problem that way. Alternatively, you could divide both sides by 3 in step one, resulting in 2x = x + 4. Then it's just a matter of subtracting x on both sides, resulting in x = 4.(2 votes)

- How do you solve the equation (39/3)+n?(1 vote)
- You don't have an equation. So, you can't solve for "n". You have an algebraic expression. All you can do is reduce your fraction to simplify the expression.(1 vote)

- Is it possible to figure out more than 2 steps at a time?(1 vote)
- When it comes down to getting the x by itself, how do you know whether to add, subtract, multiply or divide the number next to the x?? I am a little confused.(1 vote)
- how would u solve an equation like this 5b+b=12(1 vote)
- Combine like terms. 5b+(1)b is equal to 6b. Now you have 6b=12. In order to have the variable "b" by itself, divide both sides by 6, and you should get b=2. :)(1 vote)

- how do u answer a question with 6x+7=5b how would u solve a problem like that(1 vote)
- When I took college math I was told, "To find two unknowns you need two equations." So if you have only one equation with two variables, you can only find the value of one variable in terms of the other. You can divide both sides by 6 which will give you

x + 7 / 6 = 5b / 6 and then subtract 7 / 6 from both sides giving

x = (5b -7) / 6

or divide both sides by 5 which will give you

b = (6x + 7) / 5.

b = (6x + 7) / 5.(1 vote)

- how do you find the missing expression(1 vote)

## Video transcript

Voiceover:Below are the
steps that Steven used to correctly solve the
equation six X is equal to three times X plus four, four X. Step one is missing. What could Steven have
written for step one? So let's see, so this is
the original equation, they give us a blank for step one, and then we see that he eventually
gets to three X equals 12. That he divides both sides by three and he gets to X equals four. So the best way I could
think about doing this is to think, what would I do? Well if I saw something like this, my extinct would be to
distribute this three so that I could start separating the parts of this expression that have a variable, that have the X, and the
parts that are constant. So let's try to distribute
this three and see what we get. and see if that's a reasonable step for the direction that Steven went in. So if we do that, we'd
get six X is equal to, we haven't changed the left-hand side, and the right-hand side
three times X is three X. Then three times four is 12. So you get six X is
equal to three X plus 12. Now if I don't even look
at what Steven's doing right over here, if I'm
trying to solve for X, what would be the next
thing that I would do? Well, I'd try to isolate
all of the X's on one side, and if I want all the
X's on the left-hand side I would subtract three X from both sides. So if you subtract three X from both sides you would then get Steven's
second step right over here. So this looks like a completely reasonable first step for Steven. The first step is he distributes the three to get this expression,
then he subtracts three X from both sides to get
three X is equal to 12, and then he divides both sides by three to get X is equal to four.