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## SAT (Fall 2023)

### Course: SAT (Fall 2023) > Unit 10

Lesson 1: Heart of algebra- Solving linear equations and linear inequalities — Basic example
- Solving linear equations and linear inequalities — Harder example
- Interpreting linear functions — Basic example
- Interpreting linear functions — Harder example
- Linear equation word problems — Basic example
- Linear equation word problems — Harder example
- Linear inequality word problems — Basic example
- Linear inequality word problems — Harder example
- Graphing linear equations — Basic example
- Graphing linear equations — Harder example
- Linear function word problems — Basic example
- Linear function word problems — Harder example
- Systems of linear inequalities word problems — Basic example
- Systems of linear inequalities word problems — Harder example
- Solving systems of linear equations — Basic example
- Solving systems of linear equations — Harder example
- Systems of linear equations word problems — Basic example
- Systems of linear equations word problems — Harder example

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# Linear inequality word problems — Basic example

Watch Sal work through a basic Linear inequality word problem.

## Want to join the conversation?

- why I can't understand. I mad or what(12 votes)
- you mustbe old now :)(13 votes)

- Why does it have to be next to the .8 to multiply, why can't you just combine it inside the parentheses?(7 votes)
- Because if you have in the equation 0.8(d + 1.2), it does NOT equal 0.8d + 1.2 because of the distributive property. Instead it would equal 0.8d + 0.8*1.2(51 votes)

- At the end, it said that you can just 'cut to the chase,' as Sal worded it; but sometimes that can be inaccurate and the answer was extremely similar. Why would he recommend a method that's so risky, even if it is more efficient?(9 votes)
- If you have time, don't 'cut to the chase', however, if you don't, 'cutting to the chase' is probably your best bet.(6 votes)

- Hey, I don't know if it was just me, but the wording for the question when saying "d represents the number of donuts Ayumi would need to buy to pay for 1 orange juice and the donuts using a debit card" seemed a bit off and confusing for me because it felt like the question was saying d represented both. Is the SATs wording normally like that and am I wrong to think the sentencing was kind of weird. Thanks for video, just curious about the question.(15 votes)
- The keyword is 1 orange juice. Ayumi only wants to buy one orange juice and enough donuts to bring her total either above or equal to 4(3 votes)

- Why can't answer be 0.8d+1.2>4? I know the ques says that Ayumi needs to buy stuff of $4 or more but if you think more wisely the if $1.2 is subtracted from $4 then we get $2.8 and if Ayumi buys 3 donuts then the cost becomes $2.4(or $3.6 if the cost of juice is added) then the cost will be less than $4. So Ayumi has to buy 4 donuts or more for paying through debit card. Then the final cost would be not less than $4.2. So the final cost can never be equal to $4 if Ayumi buys a bottle of orange juice and the cost of donut remains constant(9 votes)
- The whole point is to make an equation that makes sense with what the question says. It says "equal to 4 or higher", so we just go with that. This equation might not apply for donuts and oranges, but it could apply for other products or situations. Just take what the question says and don't think about its answer.(7 votes)

- Hey, I don't know if it was just me, but the wording for the question when saying "d represents the number of donuts Ayumi would need to buy to pay for 1 orange juice and the donuts using a debit card" seemed a bit off and confusing for me because it felt like the question was saying d represented both. Is the SATs wording normally like that and am I wrong to think the sentencing was kind of weird. Thanks for video, just curious about the question.(9 votes)
- I'm preparing for the PSAT and he just ends the video...(5 votes)
- Does anyone know what topics are for SAT like Algebra, trigonometry or any other that would be helpful(3 votes)
- SAT in a week and I'm at Algebra foundation... I'll finish that, do Geometry and advanced math. My talent (and chance) will help for English and the rest.(4 votes)
- I got the same answer, I just don't understand what the question means when it says 'd represents the number of donuts Ayumi would need to buy to pay for 1 orange juice and the donuts using a debit card'. I thought 'd' just represents the number of donuts.(2 votes)
- It means both, but the second meaning is just a form of shortening it so it's easier to say. I can understand the confusion though.(3 votes)

## Video transcript

- [Professor] A convenience store requires that Ayumi spend $4 or more if she wants to pay using a debit card. Donuts each cost $.80, donuts
each cost $.80 or $.80 each. A bottle of orange juice costs $1.20. If d represents the number of donuts Ayumi would need to buy to
pay for one orange juice and the donuts using a debit card, which of the following inequalities best models the situation described above? Alright, so she needs to spend $4 or more and she's going to buy one orange juice, she's going to buy one orange juice and d donuts, d represents
the number of donuts. So let's write this down,
so this one orange juice, this one orange juice right over there, that's going to be $1.20, we'll assume everything
I'm writing is in dollars, that's that and then how much
is she gonna spend on donuts? Well, the donuts are $.80 each and d is the number of donuts, so she's gonna spend $.80 times d or 0.80d we could write it like that, or we could just write this as 0.8, 0.8d so this is what she's spending
on that one orange juice, this is what she's
spending on that d donuts and in order to use her debit card, in order to use her debit card, she needs to spend $4 or more, so that this thing right over here needs to be greater than or equal to $4, once again, greater than
$4, that's the or more, but it could also be exactly $4 and that's why we have the
equal sign right over here. So let's see, which of
these choices describe that? Let's see, you have .8d plus
1.2 is greater than four so before you even see if this
expression right over here is equivalent to this
expression right over here, you could see this is greater than four, we wanna be greater than or equal to four, so just like that you
could rule this one out and actually if you distribute the 0.8d you will see that you
get something different, you get 0.8d and then 0.8
times 1.2 is not $1.20 it's not 1.2 right over here,
so we can rule that one out. 0.8d times d plus 1.2 is
greater than or equal to four, well let's see, that has
a greater than or equal to but if you distribute 0.8d,
0.8 times d is going to be this but 0.8 times 1.2 is not 1.2 it's going to be .96 so 0.96, so that's not going to work out. Let's see, 0.8d plus 1.2
is greater than four, we're close, but remember we want greater than or equal to four, and then lucky for us,
this right over here is very similar, it's
exactly what we wrote up here with just the difference that
instead of writing $1.20, they wrote 1.2, so if you
just swap these two around you get, let me do that
in those same colors, you get 0.8d plus,
instead of writing $1.20 I'll just write 1.2 is
greater than or equal to four, is greater than or equal to four, so this is exactly what we had over there so I would definitely feel
good about picking this one. Now if you're doing this in
really kind of timed conditions, I would, instead of even doing this, you could go straight,
instead of just even trying to think it through you
good go straight to say well, which of these really
describes what's going on here? So let's see, we wanna be
greater than or equal to 4$, we're gonna spend $1.20 on orange juice and then the amount
that we spend on donuts is that right over there,
so you might have been able to just cut to the
chase and pick that one. Whichever way works better for you.