hi what what this will be is a little practice test using the Aleks software but I was able to get it printed on a piece of paper and it's a PDF file yours of course will be online but they're asking us to start and what I'm going to suggest here is that you in your homework log or wherever you're going to keep this is pause in a sense write down the question and work it and then I'll work it as well now part of this is to follow what they're asking the instructions the sum of nine times a number and 4 equals 8 so over here you want to write that answer and they're asking you to use the letter Y so we would write nine times y nine times the number the unknown number is y and indicates addition equals eight not we'll leave that up because we have room now they want us to solve this equation so again on your blue sheet if you're doing a test or in your notebook you're going to write 9 equals u plus 5 and you'd want to label this as number 1 and this is number 2 I'm going to give you a blue sheet that's divided so it's easy to find your work so we want to isolate the U so one way to do it again you could transpose but we're going to subtract 5 here subtract 5 there what we're doing the one side we do to the other and we end up with u equals a negative 14 so I can see they're starting us off pretty easy alright for number 3 a negative 5x equals 10 thirds now this could be a little tricky but if you recall we said whenever there's fractions multiply every term by the lowest common denominator and here this is one term this is one term our lowest common denominator happens to be 3 so we'll multiply both sides by 3 now here the threes cancel out and you're left with a negative 15 X to smoke line this equals 10 now there are no fractions so to get rid of the term or the part of the term that's with the X we call that the numerical coefficient we divide by this now notice it's negative so you have to use a negative 15 and then this all cancels out becomes a 1 anything divided by itself is a 1 so it gives us X now we know this division here is going to give us a negative a positive divided by a negative gives you a negative and we can take a 5 out of each one of those so this is a negative 2/3 and again this is the work to support your answer and again pause it to write something down alright again pause it I have written this one carefully here and this is number 4 and as I look at it definitely has fractions I want to find what is my least common denominator between a 3 a 2 & a 9 think about it and if you said 18 that is correct now 3 goes into 3 once 3 goes into 18 6 times 2 goes into 2 once 2 goes into 18 nine times nine goes into 9 once 9 goes into 18 twice so our next step is a negative 6 times 1 is a negative 6 a negative 9 times 3 is a negative 27 you equals 2 times 5 is 10 we want to get all our letters on one side all of our numbers on the so I'm going to transpose this negative six or add six bringing it to the other side makes it a positive six so this becomes 16 negative 27 you now what I'm going to do is divide both sides by the coefficient of U which is a negative 27 and that's about as far as I can go so u equals a negative put the negative in the middle there 16:27 all right if you have time to copy this down then it has fractions get rid of the fractions by multiplying each term by the lowest common denominator which is a four here and this is number five okay give you some time so now we do our canceling 4 goes into 4 once so these just cancel off and I end up with a y here 4 times 8 is 32 and 4 times 27 is 108 so again I can subtract 32 here subtract 32 or take this positive 32 transpose it to the other side where becomes a negative 32 and this then gives me this is gone now y equals 76 okay now again we're trying to model by showing you the steps in a clear orderly way I probably should have written this again here but hopefully you have room on your paper to do so I moved it up and again pause and I've written out three of them to save a little time and as we look at number six what do we do first well there are no fractions so then we get rid of grouping symbols so we're going to distribute that and we get 8y minus 2 times 9 is 18 equals 14 now we're going to transpose the negative 18 on this side it becomes a positive 18 or you're just adding 18 to both sides and you get 8y no equals 32 divide both sides by 8 we get y equals 4 now you might note I didn't show the division here and you know normally there are steps you can take shortcuts ok now I'm going to erase this because it's going interfere a little bit with my next step so we'll just erase that one but you can always go back now for number 7 there are fractions and there's three terms what's my least common denominator just give you a moment to think about that now five times seven here is 35 but two doesn't go into 35 hmm but if we multiply 35 by two we get a seventy and then each of these go into 70 so our lowest common denominator there is a 70 so I have to multiply everything by 70 and you want to pick a denominator that the denominator will cancel out with what you're multiplying each term by you're making this equation equivalent it's going to be different you're making it bigger but again with his multiplication that we do here after we divide we can have fractions that are denominators that are just two what no fractions so seven will go under there once seven will go into there ten times I will go into there once five will go into there twelve times how about 14 times yes five times 10 is 50 and four times five is 20 okay that's better and two goes into there once two goes into there 35 times so I now have a new equation negative 2 times 10 is a negative 20 equals 6 times 14 so this is a 84 X 14 times 6x and then this is just a negative 35 so if we transpose a negative 35 to this side it becomes a positive 35 and a negative 20 gives me a 15 equals 84 X I'm going to divide both sides by 84 so x equals this but notice and let me review this with you we call it the rule of threes if we add up the digits in a number this is a six and this adds up to a twelve and both of these are divisible by three so looking at something this is divisible by three so let me erase this part here three will go into 15 five times and three will go into 84 28 times so our final answer then is x equals 528 now if you put this in there they'll count it in correct but when I look at your work and see that you've done all this you just didn't simplify it I give you lots of partial credit let's clear this up here a little bit going on to number eight now hopefully you've copied it down the question would be how many terms are there well because of this division bar all of this is one term and this is one term so there's just two terms what's my lowest common denominator and I can put this in parenthesis here and the answer is a negative three so here multiplying this by a negative 3 the negative 3 just cancel out and on this side we're left with 5x minus 19 equals a negative no negative times negative will make it a positive 21 so I'm going to and and although the other way to so you can see it add 20 I'm sorry at 19 I'm thinking of what's coming up here add 19 add 19 so we get 5x then equals 40 and divide both sides by 5x equals 8 so again the process of transposing a negative 19 on this side becomes a positive 19 taking a term from one side moving it to the other and in essence what you're doing is you're adding a positive 19 to both sides all right take a moment copy number 9 and as we look at it there's four terms our common denominator this one's a little easy it's going to be 15 so three goes into there once 3 goes into there 5 times 5 once listen to their 3 times 5 once 3 times nothing there so that negative 5 times 4 w is a negative 20 w 3 times 6 is 18 negative 3 times 6 is a negative 18 W and this is a negative 45 never hurts to check your work here you know that looks good now we want to try to keep our W is positive if we can so I'm going to transpose this and here it becomes a positive 20 W so this is a 2w I'm going to transpose this so here it becomes a positive or yes positive 45 and this becomes a 63 and we divide both sides by 2 and here the twos cancel out we get W equals this now notice two doesn't go in there so you could leave it as an improper fraction okay for number ten we have to read it carefully there were this many tickets sold for a school play they were either adult tickets or student tickets the number of student tickets sold was three times the number of adult tickets sold how many adult tickets were sold so student tickets was three times the adult ticket so we don't know the number of adult tickets sold so we're going to say the adult tickets sold were a a four adult tickets this stands for a number could be fifty or sixty or whatever now we know the student tickets sold was three times the adult ticket sold so plus three a and we know the total ticket sold was three sixty so this one was rather easy but it does take time to check it out so we're gonna group like terms remember there is a 1 in front of there we don't write it for a and this is number 10 equals 360 divide both sides by 4 hey equals 90 so the number of number of adult tickets because that's what we said a was is 90 tickets okay let's clear this and raise it up actually and then set this up copy it so we'll solve it in our next step now one of the first things you should always do after you copy something on your blue sheet is did you copy it correctly and check that okay then you study you say well it's an equation with fractions so I have to multiply every term by the least common denominator you have a two and you have an eight and you might say well it's 16 no no it's eight eight would be the least so because of the grouping symbol this division bar this is just one term this is one term and again this is one term and we're gonna multiply each by eight got carried away there there that's better so here the two zoo goes into there once and there four times here we don't have anything but this is nice they just cancel out completely but we have a negative sign in front of that parenthesis now so we have to distribute four times you is for you and don't forget you have to do the second one also that'll be a negative four this is a 48 here now this is the tricky part you have a negative sign in front of a parenthesis you have to change each of these signs this becomes a negative seven you and this becomes a negative eight alright that was a little tricky that's why grouping symbols are important and doing something like this now we're gonna combine like terms we get for you - for I'm going to subtract eight from this and I'm gonna have negative seven you subtracting 8 from this these me with a plus forty so I set it up with a variable term constant a variable term constant now I want all my variables to be positive if I can so I'm going to add seven here or transpose that and this gives me 11 you I'm gonna transpose this on this side it becomes a positive 4 or ad for ad for this is 44 I'm going to divide both sides now by 11 and I get u equals 4 for number 11 and that chicks ok we can leave that there for a moment again you're pausing as needed and going back apologize for that little the step up there check your work since last week Dave drove this many miles this week he drove this many miles using V write an expression for the total number of miles he drove in two weeks well that's pretty straightforward he drove to 71 in that first week and in the second week he drove this many months and that's the answer so it's nice to have something easy it's not an equation and you know if it equals a total number then that would be something else but that's what we have so far now in number thirteen there's a couple of ways to look at it but you have to read it first the price of an item was reduced by 45 percent the original price was 60 percent so what is the price of the item now well you could take 45 percent of this and then subtracted or a shortcut would be you're paying if you're getting a 45 percent discount you're paying 55 percent of 60 we'll give you your new price again the other way would have been take forty five percent of sixty then subtracted from sixty or you realize that your new price or the sales price will be with a forty five percent discount is fifty five percent with that in your calculator and you get n equals thirty three dollars hi Philippi needs to make this many deliveries this week so far he has completed 19 of them what percentage of his total deliveries as Philippe completed well we find percentage by putting the portion that was completed 19 over the total 25 put that into our calculator and we get point seven six but that's a decimal fraction we convert a decimal fraction to a percentage by moving the decimal point over two places and adding a percent sign so our answer is 76 percent all right number 15 what percent of 60 is 57 well again the work would be 57 over 60 put that in your calculator and it gives you point nine five but again they don't want a decimal they want a percentage so after move the percent over or the decimal over to make it a percent now letter B what number is 15 percent of 80 so let's just set this up as an equation 15 percent of 80 is N or P or whatever letter you want to use well when you do that put 0.5 times 80 you get 12 all right these are some easy ones just taking your time to understand what's going on here all right let's raise it up a little high for number 16 tortoise walking in the desert he walks for this many meters at a speed of 5 meters per minute how many minutes does he walk or does it walk well here we're using the formula distance equals rate times time and we know the distance is six point two five we know the rate is five and the minutes is T for time so we divide both sides by five this ends up as T equals one point two five minutes now pause and think about these as much as needed I don't want to you know I would have to think about it a little bit too right mary has four scores on four tests what does she need on her next test so that the average or mean is 77 well what you do to set this up as you go 79 plus 66 plus 81 plus 93 and what does she need on that last test well we don't know so we'll say plus X so that her average is 77 now the question is first of all is this an equation nope because in order to find out what this average is we have to divide this side by the number of tests taken so one two three four five that's the equation so this then represents an average and we want this to be an average where this number here is unknown so what do we do well keeping in mind that this is a fraction we're going to multiply and this is just a seven-year both sides by five so here the 5s cancel out now I have to add these up subtract this from this total once we do the multiplication and then that would be what we needed on our last test all right so let's pause it and do some work here now again each cancel out I added this up and I got 319 plus X and then by timing 77 by 5 this gives me an average of 77 once I divide 385 by 5 but the total of 5 tests that each 77 gives us this so now I subtracted 319 from 385 and I get 66 so that should be rather easy to do it's been doing pretty well let's get a 77 77 is usually considered a c-plus I would shoot for perhaps a little higher than that okay right inequalities to represent the situation below and again you pause it and you're going to think of how do I write an inequality here alright to get a 10% discount a shopper must spend no less than $100 use D to represent spending in dollars so D would be the amount of money we have to spend no less than so D would have to be greater or equal to 100 all right again you had to think about that and which inequality sign and I believe they talked about no less than he equates to greater than or equal to at the airport each piece of luggage to be checked checked in must weigh at most fifty five pounds so here W has to be less than or equal to 55 all right yeah they took some thinking about what inequality sign are you going to use alright let's go on for this next one they're asking us to graph on this number line and this is in set-builder notation so we know a negative seven is there so we're going to put a parenthesis at negative seven and it's less than negative four so a parentis e there and we fill that in now I believe though in your case they'll want you to use the hollows which you are allowed to put in there the hollows are for the parentis another way of doing it would have been brackets would have been a solid dot if it were also equal to but that's not what it is so this is the answer and then write in interval notation so it'll be parenthesis negative seven comma negative for parentheses okay one more to do and we're finished now for number 20 here we copied it down it's with fractions what's our lowest common denominator well it would be 30 so this is 30 w6 goes into there once this is 5 plus 5 is greater than or equal to 5 goes into there once 5 goes in there 6 times a negative 18 we're gonna transpose the positive 5 to the other side where becomes a negative 5 so this is negative 23 now divide both sides by 30 W is greater than or equal to a negative 23 30s now I know you're wondering should I have changed the direction of our inequality sign and the answer is no you only do that if you already divided by a negative or multiply something by a negative in order to keep it correct you have to reverse the sign but not here because we're dividing by a positive ok this was just under 38 minutes or so hopefully it's helpful