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Quiz 2 (Video Answer Key)

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Use this to solve all problems from Quiz #2.

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hey guys Welcome to our first video of the Year this is to I'm going to show you how to do all the problems from your quiz so you can correct these and you can be ready for the test tomorrow so here we go this first problem I hear it's going to go kind of quick so but you can always rewind it if you need to this one right here the first thing we need to do is I need to do this work right here just need to do this fraction is inside the parentheses I want to do that first for 7/8 - 3/4 we could do the three arrows on this or we could just do a common denominator in this case for common denominator is a lot easier with a prominent Mater's 8 so I was just multiply the denominator by to and thus numerator by 2 it's going to give me this new problem right Savannah cat seven eight -3 x 2.6 over it saw 7 8 minus 6/8 equals 1/8 served so I'm going to rewrite this problem form this is one fourth Linus and then this is 1/8 you just found that out so once again the common denominators once again 8 hopefully you see If I multiply 4 times 2 it's going to give me 8 in the denominator so said if I finish this out in the numerator I have One X to witches to denominators for x t which is a minor 1/8  NS equals 1/8 Super Final Answer here the problem this one right here we did this we did some problems like this in class it's easy if you reorganize it if you notice so I'm going to reorganize this and I'm going to put 3/4 and I want to put X  12 / sky from Africa 12 hear from 3/4 x 12 member when I multiply I can multiply in anywhere I want so then I'm going to I don't know I put a place there X  15 7th  time 49 beauty of this is that I can cross divide here because it if you look this this is like one long numerator 3 times 12 times 15 times 49/4 times 1 times 7 times 1 so I can cross out anything in the numerator and denominator if they have that common multiple so if you look here I have a 12 in the numerator I have a 4 in the Terminator both of them have a common multiple of four four divides into both of those so I can divide those both by 412 divided by work is 3 4/4 is 1 the same case is going to happen over here I have a 7 in the denominator 49 in the numerator as a result I can divide both the numerator and the denominator by 7 so 7 goes into the numerator of 49 GS 7 times 7 goes into the denominator of seven here yes one time for now sharted if you know if all of my denominators are now one so all I'm going to do is multiply across the numerator I have 3 x 3 set this is what's last year 3 times 3 times 15 times 7 right all over 1 * 1 * 1 * 1 okay that's what the living on Monnet turn out right so three times three this is nine so three times three that's nine write 15 * 7 what's 15 * 715 + 7 boom boom kd3 here we go on a 5-4 this is 9 x 105 which is just 900 45  hopefully that helps next problem you can expansion box to multiply one 4 * 999 so remember the first thing we're going to do let's rewrite this rewrite 1004 as one awesome  + 4  rewrite 999 as 1,000 -1 and this is going to make our location a lot more simple here so Wichita expansion box going to be a 3 by 2 Box  I'm above the first box on the put the first problem here 2000  squash  for the second box in the put the second problem here 1000 - so 1000 x 1000 is a 1 with 6 zeros or 1 million sorry for * 1000 is 4000 1000 * -1 is -1000 4 * -1 negative 4 so if we look here let me have the positive numbers together here first I have 1 million  4000 that gives me volume  4000 facts about these two now we're going to subtract off a thousand that's going to give me 1 million  3000 synonyms of truck off for 5 1 million 3,000 -4 so we can do this along way here and we can just carry  from this is Milan way I hate it but public information West 10 - 469 - 09200 can a one here okay so there's that that problem answers 1 million  2996 easier way to look at it up here so whenever I had 1 million 3000  minus or you just back it up for what's what is 3000 - 4 it's just 2996 and then you just everything else on the end of that to finish it out so I think that's easier so once once again if you look here at 3000 -4 that's 2996 and then you just bring me zeros down to put them in their place and then you get that Exeter  sex problem  solve each equation here we go so we're going to get the extras on the right side the numbers on the last summer app for extra besides I'm going to get two equals 7X - 47 + 47 - both sides we're getting the numbers on the left so I'm going to brightest up here my left side is 2 + 47 which is 49 equals  bomb.com 7 x 3/7 are you going to get apps  47 Eagles after x equals same thing here we go there a lot of people look like they made it may be a little more difficult than they needed to these are like if you look all of these are the same thing they're all x -3 x all right so if I have negative 3 or something negative 5 or something something negative to something how many do I have totals will -3 + -5 is -8 + 12 is 4 - 2 is I have two of these total  curfew times the quantity of x minus 3 equals 24th is pretty easy to deal with divide both Meds by to not make it x -3 equals 12 then I'm going to add both sides add three or four sides Xanax is going to be 15 pretty simple try to diss the very beginning of this problem you missed the point so we can going over these a lot of going over where  some do I sperms if you didn't recognize these where life turns you probably had a hard time with this problem so hopefully if this shows up on the test on Friday you'll recognize like terms next problem this one solve the equation 3/4 x - 8 equals y 4x so we're going to solve for x so if I were to read problem it would say 3/4 times x minus 8 equals y when we're solving for x can I so once again 3/4 times x minus 8 equals y and if we remember if we if we if we solve in reverse order of Kim's hair right  remember that's how we solve equations right we solve in reverse order so we would follow this weed under subtraction and addition first division multiplication then exponents in parentheses well you can see here we have traction I have -8 of -8 3/4 x x -8 equals why we're going to undo Traction in addition first subtraction in the negative 8 in the -8 from an undo that with Edition I'm going to a date to both sides phone. so I would get 3/4 x equals y + 8 so now I need to get this 3/4 away from this axe here this is 3/4 time. So I undo  multiplication with the now that means I would divide both sides by 3/4 time I would divide both sides by 3/4 alright like this but remember dividing by a fraction is the same as multiplying by its reciprocal so that's what we're going to do here we are going multiply both sides by reciprocal Phone 7 x reciprocal and I'm going to multiply  this side reciprocal so 4/3 x 3/4 that's just a warning so one x equals over here I have under the put the Foresters in front  and I just have four thirds X Y the quantity of y + 8 cast in if I want to do if I wanted to distribute this I could I would get x equals I don't even have to on this problem I would give you credit you didn't soap if I distributed if I get four thirds why  plus four thirds times with horses State Farm 32 32 / 3 across the new Moto X cost with denominator either one of these would be correct answers  sex problem here we go so I'll be absolute equations not remember absolute value equations have two solutions okay the left side is always going to stay the same whenever written like this what's just an absolute value equals a positive number all you have to do just keep the left side the same you make it equal to the pause Chase and then we have a negative case so 3x - few also equals -7. so that's how we would do this here right here  making myself a little bit more here we go. Both of these I'm going to add to both sides Spurs first problem I would get 3x  equals 19  if I both sides by 3 x equals 19/3 or we can call the 6 in 1 ferret first and then my other solution the negative portion here I'm going to add to both sides I'm going to get free axe equal -15 / 3 taxes going to equal -5 there's my pasta what is x equals 6 1/3 or -5 sisters two possibilities so this is going to bring us to a problem here and an absolute value equals a positive number and has two solutions. So if you notice absolute value equals a positive number that has two solutions for the plug at the next problem here song this guy right here so she saw the obsolete equations what you need to recognize these two guys these this and this are like terms I have -5 times out of survival write -10 times I see that's what's for theirs their lifetimes they can combine so the reason that is important is because the first thing I'm going to do is I'm a odd turn of these  guys right here to both sides cuz I'm going to get it off the right side here phone maternity this is going this off the right side just going to give me off -5 or something antenna something over here on the left it just gives me five of these the minus 7 equals -2 absolute value by itself isolated on the west side so I'm going to treat it just like this is a variable if I promise all for it I have to have this it has to look like this on the left side before I can solve this I need to get rid of subtraction by adding  somebody get five times the absolute value of X Plus 4  the 7th cancel here equals -2 plus 7 last time I checked was five so we're going to divide both sides by 5 in America  absolute value of x + 4 equals 5/5 will be on the right is one so now I just need to set up my two equations  here's my positive case number One X plus 4 equals positive 1/4 x + 4  equals -1 just set up both equation share absolute values if an absolute value equals a positive number and always has to some Sun Vista Solutions in this case are x equals negative 3 or sex equals -5 k so there we go the solution chair I wanted to check this 3 yep that's right so next next page I was just plug in a minute my house and some mental math you can always check please make sure the correct so see her nope we've already done you next page this one how many solutions do the following absolute value so an absolute value if an absolute value equals a positive number it has recently Sheen's remember we set it up bum x + 1 equals positive 1/4 x + 1 equals -1 if you solve this if you solve this you would see that  x equals 04 search for Messi tax equals -2  first relationship now for check this out try to how many equations could you right here x + 1  sequels positive zero or yes it is already doesn't make sense right x + 1 who's negative girl what does no such thing as positive or negative zero right there's just zero so in this case you just say X plus one equals 0 that's the only solution then you would solve it and you'd find out that x equals negative one the only one at work so there's only one solution for letter C hear an absolute value always positive so no matter what I put in here for Acts  there's way that I would ever get out of -1 it doesn't matter what I put in for X because like let's just say like just for instance or let's put in the negative for 4X and if I did this to try to see if this is a solution I will get the absolute value of -3 equal -1 of the absolute value -3 - 3 equals negative one no matter what I put on the left side it's always going to come out positive in the end this is a positive number K and you can do this check yourself whatever I put in for X it doesn't matter always going to end up coming out at the very end of the problems at as a positive number cuz absolute values are always positive this is no Solutions you can't negative number  from an absolute value problem can ice next convert the following decimal fraction this is supposed to have a repeater bar over at like this nice so just to remind you this is what we did this is how he this song we're going to rewrite this that's point one 71717 right it's repeating remember then we set it equal to act scarf  so what I'm going to do is because I have to repeating numbers here I'm going to say what is 100 x x 100 x x if this is x 100 x would be 17 points right what's 100 * fat is what I'm doing right now okay what is that well 100 times there they just move the decimal places to the right so answer what your speed this the 100 x equals Andover going to do to subtract these really subtract extra 100 x  Arkansas 99x on the left on the right you can see that all these all these are going to cancel out I'm just going to head up with 17.000 so answer here for the Bible Side by 99 Jamaica tax equals  17 99  from connect  so a plus b equals what is -6/8 - 6 B so the thing is is that I need this  tavern must be in the way I can do that is if you notice both of these contain a 6  but if only factor on a positive 6 that's going to still be anything negative fracture out of -6 / factor in -6 and 1 of these terms it's the same as it's the same as dividing 4 by -6 this is what I'm saying  so negative 6A divided by -6 is just a -6 B  divided by -6 is just positive B stretch out a negative sexy gif she get -6 times than you get a plus b equals -8 -6 * -8 is 48 some Stars free simple next problem  so first offer going to reorder this problem let's put the a witch witch put it in alphabetical order here Sonic going to factor out a latest ran out of the first few times when I do that I'm going to get an A+ because I got to have an A+ be here right also here boy factor out of 9x + 9y to give me an x + y well if you said 9 you're correct okay so I have to make it look like this I need a essay + B I need an X + Y and I got that so A + B tells me up here is -9  x + y it tells me up here is positive 5 so this is 90 negative 10 times a day turns positive 90 + 45 in this equals 135 phone next Rodger gets $40 per day as wages and 400 is commission for every pair of shoes he sells in a day his daily earning goal is $112 write an equation to determine how many pairs Rodger muscle in a day to meet his daily earnings goal will check this out I'm just going to let's just say she gets 40 bucks no matter what right so what if what if he sold one pair of shoes if you sold one pair of shoes he get $4 $0.50 x one pair of shoes right so how much would that can that would be 40 + 450 which is $44 50 Cent right so what if what if he came in and you only sold a few pairs of shoes well Starz issues is 2 * 450 which is $9 so that would be $49 right see how many shoes has to sell to meet his daily earnings goal was daily Ernie goal is $112 he's not even close to that right what if you let's just say what if  what if Rodgers sold 10 pairs of shoes how much would that be that would be 40 what's 450 * 10 + $45  that equals $85 I could just keep guessing and check I'm here, until I got there I guess I could just add 450 I could just say he sold 11 service she's 12 prayers and she's I just keep going until I found it out specials in here feels right and if equation okay well  which number here in in my the equations I set up what number represents the number of pairs of shoes he sold will it simple so it's $40 plus these numbers stayed the same on all three of my equations if you look $40 + $4 + $50 $6.50 so but what change is the number of pairs of shoes you sold so this case and says write an equation determine how many pairs of shoes Rodger must sell we're going to do just put a key here instead of a number right that's going to dictate the number of pairs of shoes you sold for 40 + $4 $0.50 times the number of pairs of shoes he sells equals and his daily earning gold was $112 so that the equation here okay this is equation the sit sit up Anna now all we have to do to figure out how many parents he has to self meet his daily earnings goal is just solve this problem here 40 + 450 I'm going to write as 4.5 P equals 112 child it truck 40 from both sides  you going to get 4.5  as part of the shoes equals 72 you can divide both sides by 4.5 I'm not sure  472 / 4.5 is so let's do the math over here and 72 divided by 4.5 search I'm going to use division trick here right move this over move the decimal over one place 45 goes into 720 this is the same problem is 72 / 4.5 45 Goods in 272 once chrome truck. Spring a 02 C70 3-45 is 27 than the zero down so let's see I think this is 6/6 times 536 times 40 up sis is 20 up soapy equals 16 pairs of shoes and if you if we plug this back in our original member of the beginning I was saying we we had all those equations flipsy  $40 + $4.50 x 6 pairs of shoes right this is 4450 * 16 is 72 like yeah Sissy 16 pairs of shoes and 16 pairs of shoes that was our variable so  Fright Night KDs one step inequalities pretty simple I treat this just like this I treat a treat it no dip there's only one right so I'm going to divide both sides by for here and we'll talk about the expression in a minute if I were solving this with the equal sign get that I don't change anything here let's do the same thing the reason why is because I'm dividing by a positive so the ne quality stays exactly the same the inequality  stays the same because I divided by a positive numbers I divide a positive number there for the inequality stays the same next problems now what you can see here on multiple I'm I'm going to multiply both sides by an I'm going to multiply both sides by the negative reciprocal here by the reciprocal will multiply both sides by -3/2 time now multiply both sides by a negative  the inequality is going to flip from so this is just one acts quality instead of pointing to the left will point to the right like this now negative 10 negative 10 times 3/2 K but she's our division trick I should you earlier to divides into the numerator and denominator to divide Turn 5 x 3/2 once -5 * -3 is positive 15 sister's actions greater than 15 sex so we have 1/4 greater than -8 now will I be multiplying or dividing by a negative I will not I will be * positive inequality will not change the reciprocal of 1/4 is 4 / 1 I'm just going to write it as for  so this just ask is greater than -8 * 4 is -32. Once again I multiply both sides by a positive there for the ending does not flip next problem -7x is less than or equal to 14 this is a simple survival Side by negative should I multiply or divide by a negative yes I did there for the inequality instead of pointing to the left point to the right 14 divided by -7 is -2 and there goes our first video

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