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Pre-Algebra - 4.6 Writing Equations

Added Jan 13, 2021 •

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Be able to write an equation (2-Step) given information from a word problem and solve it. Solving a 2-Step Equation: (Pre-Step 1) Simplify, if possible, one-side of the equation - by combining like terms, distributing, etc (Step 1) Eliminate the Constant from the side with the Variable - Additive Inverse (Step 2) Eliminate the Coefficient - Multiplicative Inverse

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write a two-step equations what it means is read the problem and write a two step equation to solve verbal Problem by writing and writing and solving a two-step equation that's just the main idea so first you know how to create a two step equation okay words that that you supposed to solve it let's read through this and do a mental math chicken fall on Medi salt and Ivy spent a total of $22 for lunch IVs lunch cost $5 more than medicine so I'm going to stop if you got the thing to look it's about setting it up we do not know we do not know how much each person pay but we can figure that out so we know spent $22 for lunch together that's the total and medical and IV so here's a clue right here we know that Ivy's lunch IVs lunch is equal to $5 more than many Sol's so obvious lunch equals $5 more than medicine has lunch and let's look at this IVs lunch equals 5 plus medicine and how much does Mary Saul's lunch cost we don't know and this is where people get stuck putting in a variable and we have two unknowns but in algebra especially Algebra 1 you even though we don't know what Ivy is ivy can be considered the variable I and Marisol can be considered the variable M so this right here $5 more than met Esau and plus 5 so IVs lunch equals plus $5 more than maybe sauce lunch lunch it's just m but this right here wish people get mixed up no cares you can always rewrite terms of one variable from now all the way to calculus pass calculus that's your main goal if you got other variables how do you just write an equation with just terrible because we know that I equals m + 5 here here's where people make a mistake 22 that's how much I paid for lunch that's IV plus Maddie saw but that's two variables now we can't do anything instead of writing and I we know that i-gos m + 5 and if you read m + 5 is the word IV for the name Ivy Ivy and Marisol spent $22 on lunch IV spent $5 more than that he saw how much do they each pay for lunch when you find what Medi Saul paid you figure out what IV paid by adding 5 to hers so this is our equation right here 22 + m + 5 equals and again here is your equal sign wall I mean sorry I crunched everything together clean up your one side if you can before so Step 1 simplify if you can sew 22 equals m + 5 + m if you read it out loud and plus 5% you don't need to read the parentheses that's just there to help you see if m + 5 + m that is 2 m + 5 Next Step get rid of the constant it's a plus five to get rid of it you subtract 5 22 - 5 what is that 17 and then 2 m we bring that down 2 m / 2 m to x m so the opposite is to divide 2 / 2 is am so Maddie song paid what is this half of $17 850 Marisol paid $8.50 that means what did Ivy pay Ivy paid $5 more she thought she was fancy so I V equals m + 5 which is 8.5 + 5 1350 is what I be paid and look at this we can check our answers 1350 + 850 that's a Dollar carry a 1/8 + 3 is 11 + 112 + 1 $22 don't complicate things you guys are complicating things by one step at a time and look at me and I yell at you small Riders a try and save paper you guys have issues because you're you you cramp while you're working you can't see it you can't do anything notice ugliest my handwriting is I'm still able to find what I'm doing because I spaced it out so I can see use your paper it's just paper it's not like it's you know food paper let's go look at let me see love you let's translate this and we'll work on it so I'm going to do one you're going to do one so it just shows us so Translate this right here is just learning how to read and pretty much done with that Zach has six shirts Zach has six shirts this is less than no one has less than remember when you have Anna and this six this means six shirts this Zach has six shirts this represents his six shirts is in math means equal less than remember when you see less than is not the greater than equal sign or less than sign is means equal is less than is there is 4 less than twice the number of shirts and that Xavier had so what you do rent remember until you see the phrase then with the add or subtract you flip them around this is what is this this is six six schools 4 Less Than so - 4 you flip it instead of 4 - 4 Less would be 4 - before less than is -4 cuz you're comparing it to a number that came before it less than the word that means you're comparing that's Lexile 4 less than less than what less than this number that should have come before so this is 6 is 4 less than twice the number of Shirts n that Xavier has so and stands are the numbers words David has twice means two times and there's your equation you saw me or if you want see that's up to you so six equals 2 and -4 and if you want and here's the thing read instruction that it's a solvent know it just said translate but if you saw that that's fine translate each sentence into an equation so you need to know how to translate it into an equation renstar they're always going to give these type of questions you always get these type of questions on the standardized test translate which one now let's say this doesn't appear on there remember multiple choice sometimes your answer doesn't appear the way you wrote it down always know how to rewrite your answer to one of the possible choices if you rewrite it and then still none of choices are there then something's wrong on a multiple choice test never ever say my answer doesn't look like any of these I got it wrong and start over always check to see if there's an equal version by the way you could write this 2 + -4 equals 6 same thing and if you want to add 4 and solve it let's all that for the heck of it too and equals 10 and equals 5 6 equals 2 and -4 so think of this savior Zack has six shirts this is 4 less than twice the number of shirts that Xavier had so twice the number of shirts Avery has so here's an end stands for the number shirt zebra has twice that is 10 4 less than 10 is 6 so it matches up its logic reading it out loud so right here try this one out on your own we're going to go get something to give you just write down the equation we're not going to solve it I just want you guys to translate it correctly will solve it later we'll do another one so for more than three times a number X is -26 give you 30 seconds if you finish type it out what did you get what did you have for your equation so translate this on your own put it in the chat so I know who's trying to do the and who's just watching a video who's watching you know you're wasting time watching one piece in the router or whatever who cares Castlevania still haven't watch that very close very close I still give you full credit for that one and I'll explain why don't solve it just give me the equation alright almost everyone has the correct remember so why do you guys want this you went left to right so you went for more than and because it's not the phrase is more than it means Plus and inequalities that the next chapter will show the differentiation on chapter 5 so bored of that means plus three times a number X 3x + is means equals -26 now because it's Edition I'm not going to take away points but if it was a traction you would have lost points anytime you see the phrase the word then connected the plus or minus need to flip these two components not the equal sign it still equals -26 yes keep X is fine if they give you a variable use the variable they asked all right 3x + 4 even though its equivalent is the better and when it's Edition I'm never going to take away points cuz if they're equivalent but you got to watch out anytime you see the word that you said to look up here less than four less than twice a day even though the word for came before in the front of the sentence it's in back because of the word Dan you're comparing its Alexa thing Edition doesn't matter if the word forget the variable 3 + 4 equals 4 + 3 but when it's subtraction 3 - 4 equals negative 1/4 - 3 equals one so when subtraction the order does not addition order doesn't matter so that's why these are still equivalent I wouldn't take any way points for it but need to know when you have the work then you got to flip it all right and not going to trip but know that certain situations it will matter on the test if you had both of these it's like on the SAT of that the ren Star both of these exist and it only wants one answer this is the right one this would be the wrong one always read all the specialist that some of them ask for more than one answer it'll say which are equivalent and to the correct answers so it's asking for more than one but then if it says which is singular which is the right answer and be this one so watch out for that alright let's go look at B 8 so same concept 8 more than you know all these vocabulary words more than so that means more that eight more than plus eight notices not 8 plus try and get it in order eight more than so + 8 the quotient understand what the question is the quotient of a number Y and negative three is negative is means equal -24 the quotient of a number y in3 y / -3 + 8 equals -24 with that said an equivalent version cuz you're my any fraction and negative so I can go three places so you can have negative y / 3 + 8 but this is not the translation of that is a translation is y + -3 the question us odisha the correct one this is equivalent won't change the value it will not change the value of y but this is an equivalent version and the only other one there is is if the negative is in the middle alright so take 30 seconds out and do be Hannah has 24 stickers this is reading this is 6 less than twice the number of stickers n Molly has translate that right there little bit more complicated but still same thing 32nd South put it in the chat when you think you have the right answer I'm getting a lot of different answers on this one but everyone started out correctly this is what is this the 24 watch out watch out so this is translate so some of you guys are giving me an equivalent version setting equals 24 but it's 24 equals this is don't solve it just give me the expression this is the 24 Hannah has 24 stickers 24 6 less than whoops watch out less than we know it's a minus and then 6 this is 6 is less than twice the number of stickers and Molly has twice the number n watch out less than remember to work if it was 6 less twice then it's six minus the word so there's less versus less than let me know they don't show that in here and that's why this book is kind of poopy but let me give an example alright so here are two different examples six less than 7x less than 7 x + 7 it is viable but it's not the translation remember you want a translation is literally point-for-point so it's equivalent but it's not the same one so this right here is less than 7 so the phrase less than mean subtract but seven needs to come first X is less than x less than 7 less than means this had to come before X7 is that right there show same thing with more than but less subtraction is the more important to deal with so pay attention to those right there and then right here let's go to the last one I don't want to waste paper cuz I went around the circle let's spokes so Jeremy has 30 baseball cards which is 7 more than 3 times the number M Michael has so Jeremy has 13 baseball cards which is another pronoun is equal 13 equals 7 more than we know what's a + so seven more than + 7 3 times the number m and this from you all can solve and simplify so that's where I'm not tripping so try this last one down here on your own the quotient of a number and 7 increased by 6 is equal to I need you on right here I don't even know that matches up with that one but if you think you have the answer or when you have the answer put it in the chat a quotient of a number and 7 a quotient of a number and 7 increase to buy 6 is equal to 12 yeah that's right good good not too complicated guitar body good excellent check your sign said your sign it's a good Hoops but not to watch out so you got a lot of guys do common mistakes just writing or typing in one little thing you got to think what happens if it was a test and you weren't you know you didn't call and you went through it you like I didn't catch that but was little mistakes change and a plus answer into a C+ answer watch out it's still so the quotient means division so I'ma write two ways quotient means division of a number n and 7 so n / 7 and notices are, that's how she that's a group next thing and / 7 increased means Plus is equal to 12 all right that's one way to ride it but remember you can write the vision as a fraction and divided by 7 is the same thing as an over 7 + 6 equals 12 which one is correct cuz that forces you to put like in a . This is better but that's just as good and there there's no I would not take away points for this one and watch out why you guys put quite a few guys put a plus 12 it's equal so it's simple little things like that just take away easy points what you should have had all right let's go example to its not too many examples next one yeah almost done almost done so you got it let's look at this let me cover this up and we'll go bit by bit and we'll compare with my work to theirs one father was 20 9 years old when Juan was born this year the sum of their ages is 53 what's find their ages right now so Juan's father was 29 years old when Juan was born sowon is just younger than his dad so when was 21 father so once father was 20 and there's actually two ways to set it up so I'm going to do this so one's father yes I'm going to go to JF for one's father ones father 29 so let's salute is 1 + 29 so remember 1 + 29 was once father's age and then how old is Juan Winans just one so J + J + 29 1 + 1 is Father's Day is 53 here's another one though here's another one before I going to do it in blue so God is actually ones father - 2018 why is Juanes father -29 that's all old one is whatever he is 29 years to track from his dad so that the other one what's the other one wants father Juan's father plus Juanes age that's not a 50 that's a j that's a Juan's father plus Juan's father - 29 equals 53 ones and subtraction one uses one as the variable the other one uses one's father as a variable we're going to get the same answer in this right here's would kind of make some some problems hard which side do you take that's all that you need to make a choice this one I used one as though what I'm trying to figure I'm trying to find wands Age first this one I'm finding one's father Age first so notice one becomes a plus or minus answers read this J + J + 29 equals 53 if you listen no it doesn't matter okay good good good good another way you can wrote this some people set up a dozen Mater the J + 29 is in front or behind watch let's read both of these J + J + 29 J + 2 9 + J same thing and when you read them both out loud we know there are equal to 53 you hear the like terms J + J + 29 variable the variable J + 29 a variable plus constant plus variable 2J + 29 and then we get our two step equation first you simplify one side if you can come by my turn now let's get rid of the constant opposite of + 29th Track 29 2 watts equals what over subtracting hahaha I almost messed up I cut myself for 13 - 9 that's a 4/4 - 224 and then two wands Eat24 but I want one wants by / 2 1 is equal to 12 years old Juan's father is 29 more than 12 wants father equals 12 + 29 what's 12 + 2 9 29 years 01 + 29 is one's father 12 + 29 what is that at 30 40 41 what's one plus ones father 12 + 41 equals 53 checking or answer what is 12 wands father is 41 one plus one Spa 53 let's check this right here so instead of finding Y on I'm going to find Juan's father's age first wants father plus Juan's father - 29 we get to Hawaii notice instead of reading JF as JS I read it as wands father it helps to read it as that thing to Juan's father -29 equals 53 and to get rid of the step one step 1 simplify one side of the equal sign step to get rid of the constant let's 29 twice once father is equal to 12 carawan 782 on vs. wants father double wants father is 82 but the best / to Juan's father's age is 41 same thing and then was fine one one is what one is one's father - 29 Track 29 here equal 12 + where did the 12 + 41 so which way is better there's no better way that's the whole thing what you guys got to understand about Mass we all think differently love you guys Wanda page some of the guys went with Juan's father age we all think differently is called perspective this is like in life we all have different perspectives on different things that's why it's called an opinion but when it comes it's which one you see first to do first next level of math so on those are all those questions those complicated stuff they ask 20 minutes at a time on the essay on the S back test the state test they're asking ask for both methods there at them they're going to say all right you saw that one way solve it another way and that she's kind of so let's say you want to read when you're done they're going to say all right using the same fax show me which one of these is the show me another way of doing the same problem and you have to know that one that's the that's going to hear this is your your your CNB student to that and even an A- for you to be considered the A+ Plus student how to say you need to know both of them that's so this is okay if you just know this great you're going to succeed no matter what but are you the Super Genius he had an elbow that's the level of question that's on the S backstage all right let's go look at and look at it they only went into the + 29 I set it up differently alright guided practice so here's number two I will get this before we go on the words for is total equals or is equal to when you translate sentences into equations so this one you are doing disha saved $3 last month this month she saved $8 more than three times the amount she saved last month she saved a total of $141 these two months write and solve an equation to find out how much she saved last month take some time I'm going to give you were finishing up with this I'm going to give you sometime to do this and while I do this I'm going to get out of the screen because you are correct at the fix. yeah the due dates keep on working on this try it out on your own and your test this is pretty much you know I'll give you a couple of plane problems and a couple of word problems that is Thursday yes you can use notes so I would use no attention to organize your notes so you don't have to look we wear for your stuff and you need to know how to print your take a picture and send it in if you don't do that I'm sorry you're going to have to do a retake during academic support for makeup credit if you cannot turn it in on time Thursday does next week's RN star that's why I wanted to finish it up this week so you don't have to do the class with your correct I I got to fix the class Rick there it is solve it with a or b what is okay today what is today pause my thing on master all right alright let's see you guys are typing stuff in let's go Checker answers alright seditious save D dollars last month this month she's 8 more than three times the amount you save last month so this month this month equals 8 more than so ain't more than three times the amount last month so three times the amount left three times the amount last month is 3D so she hasn't so deep for these two months she has saved the total of 141 now so look at this month last month was just deep right there so paralyzed $141 let me do the other way around cuz most you guys went this way so this is this month this month is the thing this month plus last month equals $141 so this month she saved eight more than three times the amount you save last month she saved a total of $141 write and solve an equation that has bulk there the most you guys had this which is actually okay I would give you a point and a half total cuz now because you forgot about last month and the total and this problems poorly-written but because you forgot this your answers even if you do all the work correctly matches going to be off so right here for D + 8 equals 141 subtract 8 what is that last 3 months we got to do that so that goes into this what is that three times we get 12 13 we get three again we get 12 we get one we get a zero bring that down we get and we get to which is 8 and we subtract me a 2-0 bring that down for goes in a 20 5 * 33.25 + 9 how much is saved last month 33 points two decimal places so this one it was kind of a messed up problem so yeah this is a pretty challenging question right here and go over the verbal let's just walk through this right here two step equations so let's go get this Logan collected pledges for the charity walkathon he will receive total contributions of $68 plus $20 for every mile that he walks so no matter what 68 bucks is a constant changes how many it's a walkathon how many miles he walks so how many miles did he walk we don't know but how many miles does he need to walk if he needs to raise 348 so no matter what he's going to get 68 bucks and it's $20 for every mile so $20 for every mile choose the variable M but he wants to do this is the minimum goal what is it to get 348 it's about reading and setting it up you got to know what's Constant and what's change it what's the constant what's a coefficient you need to know that get $68 no matter what plus $20 for every mile that means is $20 section is always changing because of how many miles so you need to read what's the coefficient what's the constant yeah I guess all that look at this he already raised 68 bucks he can raise another $20 per month so he reaches 348 need to find a hobby how much does he get with no miles at all $68 one mile in a 24 68188 two mile you get the pattern so you set a pattern and then eventually figure out all right there's your equation what's 68 subtract and equals 14 and that's all it is it's just organizing your thoughts so you got to Saint Louis Charles to Jasmine Bostic CDs all same price so 6 we don't know what the price is 6x the tax on her purchase was $5.04 the total cost was $85.74 was the price of each CD so you subtract the tax and then divided by 6 it's so you know that's all it is classwork / homework will classwork / do today is one through five. So one three five and six for Palms so 1 and 3 all you're doing is translating there's no work involved just write down the equation so 1 and 3 translate number 5 you got to solve number 6 that's not in this one number six is it in your answer guide you got to show me the answer hinson's hits 04 problems that's 12:30 get to 12:30 but one and three you could do in like a minute number 5 you can actually do pretty quick that's pretty easy number 6 months and then homework let me see what the homework is I forget what the homework is so check your answers so 1356 that's a class work homework starts I think it number 7 let me double-check what I had it at what's the class work and if you didn't turn it in if it's already turn in your turn in so start on the homework once you've uploaded it homework 7 to 17 21 + 23 so yeah so seven 2:17 r2779 11:30 15 17th at 6 21 + 23 7/8 problems so 21 and 23 kind of a challenge question 23 is definitely a challenge question yeah my mom just left so that's why I can't send them to work you will just do it later and thanks for letting me know and I'll give you credit for it so I am going to you Westside this right here so 21 you read it at all help you set up 21 is very important so these are common questions you're going to get on the S back and all these repetition test show an example of two consecutive even numbers is 4 + 6 they can be represented by n + n + to find three consecutive even numbers whose sum is 30 so I'm not going to use consecutive I'm just going to go consecutive numbers consecutive means one after the other think about that so I'm going to help you set up 21 but instead of three consecutive numbers add to 45 what are they what are the numbers so unlike consecutive even number or consecutive odd you count by 2 so the first number is for to get to six I got to add the two to get to eight I got to add another Les 8 subtract 8 so consecutive numbers I don't know I don't know what these numbers are but if they're three consecutive numbers my first number is n that's one number after the other my first number how do you get to the second number you add one how do you get to the third number you add to first number second number third number they add the 45n + 10 + 1 + 10 + 2 equals 45 you just combine like terms is two step equation same thing let's go but that's different that's consecutive numbers that's different from this three secutive odd numbers add to I'm just making something up on hundred 35 what are they what are the numbers so word problems the thing is how to set it up I don't know what my first number is but I know it's an odd number but how do you represent that you can't you just write a beer is my first number this is my first odd number the next number would be even if it's consecutive but I want to get to the next odd number that means I would have to add to odd number here's my second odd number add to get to the next odd number to get to the odd number after that I would have to add to to this so the third number needs to be n + 4N + + + 2 + + + 4 equals 135 and that's what it mean these are common questions so I will Tawana preppy just in case this ends up being on the Run start that's what it means to be consecutive odd consecutive even cuz you add to to get to the next one but if it's just consecutive one number after the other you add one each time think about this this equals I add one to get to this one I add one to get to this one that's and plus one plus one you always add one or ad to read carefully what consecutive means

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Pre-Algebra - 4.6 Writing Equations

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