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### Course: Operations and Algebraic Thinking 222-226 > Unit 2

Lesson 3: Interpreting linear expressions- Interpreting linear expressions: diamonds
- Interpreting linear expressions: flowers
- Interpreting linear expressions
- Writing expressions word problems
- Writing expressions word problems
- Interpreting negative number statements
- Interpret negative number addition and subtraction expressions

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# Interpreting linear expressions: diamonds

We match the expressions to their meaning in this example. We're reinforcing our knowledge of linear expressions. Created by Sal Khan.

## Want to join the conversation?

- I'm confused. why is there more then one way to do a problem. so annoying.(0 votes)
- I think it's awesome for there to be more than one way. Then you can pick out which way is best for you and then the whole problem will be easier to solve.(34 votes)

- When Khan Academy makes a Borderlands reference(21 votes)
- seriously, i am losing my mind right now(16 votes)

- What is really a linear expression?(0 votes)
- Okay, because nobody has been able to expressly define what a "linear expression" is, but rather they have been defining "linear equation" for you, I'll try to come up with one for you. I can't find any readily available definition of "linear expression" online or I'd direct you to it.

So here it goes: A linear expression is one that has a variable in it. Also, no variable is raised higher than a power of 1 or used as a denominator. So you can't divide by a variable.

So if a linear equation is commonly expressed as "y= mx+b", a linear expression would be expressed as mx+b. (by definition an expression can't have an equal sign in it or it would be an equation)(42 votes)

- This unlearns everything I learnt in elementary(7 votes)
- What did you learn in elementary? There is no such thing as a pony made of diamonds?(8 votes)

- At1:34, when Sal put the three other tiles into the "not used" section, one tile was 0.75p. This made me think that another way to solve the total bill could have been 2p-0.75p. That would have simplified to 1.25p. Is my way of thinking also applicable to the problem?(7 votes)
- What does 2P - .75p mean? 2P would be the cost of two ponies, and then you would have had to add 25% tax so that would be 2P(.25) = .50P, so cost of 2 ponies would be 2.50P, divide by 2 to get 1 to be 1.25P. .75P has no meaning within the context of the problem that I can figure out.(7 votes)

- Wow, this is harder than it seems o.0(8 votes)
- so if the tax so impotent why did they just do nothing(7 votes)
- 'Cause it's Khan Academy!(3 votes)

- does anyone know how to switch ur avatar lol 😂😂😂(7 votes)
- how did jack afford the diamond horse?(4 votes)
- what does this mean and can any one explain it differently??(3 votes)

## Video transcript

Handsome Jack is buying
a pony made of diamonds. The price of the
pony is P dollars. And Jack also has to pay
a 25% diamond pony tax. Match the expressions to their
meaning for Handsome Jack. And they say
multiple expressions may fit the same description. So in this bucket, we have
the price of the diamond pony before tax. Well, they already tell us that
the price of the diamond pony is P dollars. So that's P right over here. Now over here, they say the
amount of tax Handsome Jack pays. Well, he pays a 25%
diamond pony tax. So whatever the price is,
he's going to pay 25% of that. Or another way of
thinking about it, he's going to pay 25% is
the same thing as 0.25. So 0.25 times P is
the amount of tax he's going to pay on
this diamond pony. Now, they say Handsome
Jack's total bill for the diamond pony. Well, he's going to pay P for
the pony plus 0.25P in taxes. So that is this one
right over here. P for the pony plus
0.25P for the taxes. So that's that one over there. But if we look at this, you
could view this literally as 1P plus 0.25P's. Well, that's the
same thing as 1.25P. So that's the same thing
as this right over here. So it's 1.25P. And these other three
don't seem to fit in any of these categories. So I'm going to put
it into the not used. We're required to
categorize everything. So let me put this
in the not used. It's falling off the
screen, I realize. Let me put this in the not used. And then let me put
this in the not used. Let's check our answer. We got it right.