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2 study guide *better

Added Oct 16, 2019 •

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but we are working on the chapter 2 study guide I'm so the first questions they need to visit again and office today to discuss your class schedule you are told to stop by anytime before 10:30 a.m. or after 150 is currently 924 going to write a compound statement so if it's 9:20 the 10:30 you got an hour and 10 minutes so you're either waiting you got a lesson an hour and 10 minutes to wait or if you count to 150 so that's going to be four and a half hours away so if you add 4 and 1/2 hours to 9:20 to get 150 so the answer is let her be it's going to be less than an hour and 10 minutes or it's going to be great in 4 and 1/2 hours cuz you're either going to see it in your counselor in the morning session for the afternoon session so that will be it so number one will be letter b okay question number two so number two we're going to solve the inequality now even though it's multiple choice we're still going to take the time to solve it out see you at the absolute value of 2x - 5 is less than or equal to and so absolute value left would be the and statement so we're going to split this up as 2x - 5 is less than or equal to 5 + 2x - 5 is greater than or equal to negative 5 we're going to solve this both 3 to add 5 to both sides 2x is less than or equal to 10 / 2 x is less than or equal to 5 and + 5 over here 2x is greater than or equal to 0 divided I do still 0 greater than or equal to 0 so greater than or equal to 0 less than or equal to this is an A and so it's going to be everything in between 0 and 5 so we're going to have closed circles cuz we're including both of those and then shaded in between that was question number two okay number 3 is another solve and graph so it's 3 x absolute value of 4x - 2 + 2 is less than or equal to 8 and went over a lot of questions like this in class we want to get rid of the outside stuff first before we split it up so we're going to -2 the recopy everything is less than 6 / 3 and now we have absolute value of 4x - 2 is less than or equal to 6 divided by 3 is 2 absolute value lesson so this is another and statement for the right both of them for X-Plane is 2 less than or equal to 2 + 4 x - 2 greater than or equal to negative 2 we're going to solve for both so we're going to add to get 4/4 you get taxes less than or equal to one and over here we go to add to for X is greater than or equal to 0 / 4 0 / anything is still 0 so access less than or equal to 1 and greater than or equal to 0 so this is going to be everything between 0 and 1 closed circles because of the equal bar and sit in between okay question number for solve and graph the 2x + 5 is less than or equal to negative 3 or 6x - 5 is greater than or equal to 7 so the or statements were going to solve them both and then grab them both on the number line so we're going to -5 both sides 2x is less than or equal to negative 3 minus 5 is -8 divided by 2x is less than or equal -4 and then over here we're going to add five free copy everything 7 + 5 is 12 divided by 6 so we have in this is or axes less than or equal to negative 4 or X is greater than or equal to 2 so when we scan so it's going to be less are equal to -4 so close that -4 shaded to the left closed at two shaded to the right okay question number the nother or statement so x + 4 is greater than 0 or 32 is less than or equal to negative 4 borax so I can eat it we're going to solve both of those / X so we're going 2-4 so X is greater than -4 over here we want to solve for x it's on the other side that's okay we're going to divided by -4 and because we divided by a negative we're going to flip the inequality 32 divided by -4 is -8 is greater than or cool to text soacs is bigger than -4 and if you read this backwards from right to left cuz you want to read in terms of x axis equal to Negative X the smaller points on the X so greater than -4 open circle at -4 therefore does not make that through so we're not that is shaded in feed it to the right and then we have a closed or Glatt -8 is that equal bars a regular state it and that is shaded to the left okay number 6 given the graph write the inequalities so you should have gotten let's say it will use x is greater than 2 open circles on the two you could flip it around and say 2 less than x peso X is greater than 2 or you 2 smaller than x but the bigger part than the X either one number 7 you have a closed circuit 3 stated to the so act is less than or equal to 3 so the small point should be on the axe you could have written three greater than or equal to X okay question number 8 is another graph the compound inequality on we can write this in two ways so we want everything in between -1 and 5 so we can have negative one and they're open circle so no equal bar is less than x is less than 5 if you wrote those two statements with and you could have access greater than -1 and X is less than 5 now if you wrote it out with a two statement and you have to write the word and Cape question number 9 for cute is greater than -28 so you're going to / 4 2 song so Q is greater than -7 so that is going to be a open circle at -7 and she did to the right phone number 10 you have a 9 is greater than p over -3 divided by -3 go to undo that divided by -3 you're going to * -3 and remember any time we multiply or divide by a negative you're going to flip the sign -27 is less than what that piece so when you saw for this really if you read this backwards p is greater than -27 so you'd have a open circle at -27 shaded to the right a question number 11 you have 4 + + 3 is less than 610 + 8 - 2N it is multi-step inequalities now on the right side there's two and turn so combining like terms let's go to be 4n + 8 on the right see if 4 + + 3 is less than 4 in + 8 get rid of the endzone once I know when you do this is one of those weird situations all the go away so you get 3 is less than 8 that a true statement or false statement will 3 is smaller than 8 so that's true that means that this is all real numbers can plug it in any number you want for n and it'll be a true statement okay question number 12 you have four piece is less than 60 + 12 so I'm going to -62 the other side you get Negative to P is less than I'm going to divide by negative 2 ran out of room here and I'm going to flip the sign so you going to have key is greater than 12 divided by -2 is -6 30 is greater than -6 the open circle at -6 shaded to the right okay question number 13 you have five parentheses p -1 is greater than 60 - 7 they use distributive prop 5 P - 5 is greater than 60 - 7 I am going to mine at 6 to the other side so we can end up getting -1 - 5 is greater than -7 add 5 to both sides -1 p is greater than -2 divided by -1 and flip the sign soapy and less than so you're going to have an open circle at two braided to the left okay question number 14 you have 5n + 3 is greater than or equal to 4 - 6 - 5 I know that confused a lot of people on that last quiz so that minus in front we're going to remember that's really just a -1 we're going to distribute that literary copy that so 5n + 3 is greater than or equal to 4 and that's going to change that to all minus 6 negative times negative positive + 5 + t-shirts on the right 4 - 6 + 5n and then let's rewrite that 4 - 6 -2 plus 5 in RI copy everything get rid of the eye on one side and another weird situation cuz all the ends at those go to 0 to get 3 is greater than -2 so this another one is it true or false is 3 greater than or equal to a negative to positive negative so that is true so that is all real numbers remember if it's false then you say no solution 13 is a compound inequality and statements -1 is less than C + 2 is less than three solutions perceive that make that true so -2 to all three sides + -1 - 2 is -3 is less than seed is less than 3 - 2 is 1 so honor number line I'm we're having all the solutions between -3 and one positive one so it should be open circles and then faded in okay question number 16 you need to earn at least $75 you earn $6 for each hour that you write and solve an inequality that represents the number of hours H that you need to work I think there was something like that about the number of hours if you worked in one of your tasks so if you need to learn at least it's $75 you need to learn the 75 bucks or you need to earn more than that that $5 so if you are in Six Flags for it for an hour you need to earn at least $75 so you need to make sure that you earn a bigger amount than 75 or equal to that amount of 75 so at least 75 so at least is actually greater than or equal to and then to solve for that we would / 6 both sides so age is greater than or equal to a 6 * 11 is 66 so 6 * 12 we can double-check that so sick that gives you 72 with the remainder so 3 leftover so36 would be 1/2 so 12 and 1/2 275 / 6 will give you 12 .5 so the number of hours you worked has to be greater than or equal to 12 and a half hours to make at least seventy-five bucks hey last couple questions tell whether the solution or tell whether the value is a solution of the inequality so as + 6 is less than or equal to 23 you want to know if 24 is a solution if you could definitely solve it and see if 24 would be shaded number line but we can actually fight in 24 and Izzy is it true or is it false so let's plug in 24 so 24 + 6 is less than or equal to 23 between 4 and 6 is 30 is 30 less than or equal to 23 know that is bigger 24 is not a solution so number 18 you have same thing 4/3 8 is greater than or equal to negative 8 and you want to know is -3 a solution so people know it's not thoughtspot -3 so you have four thirds * -3 and me to put over one is greater than or equal to negative 8 so any you do 4/3 * -3 the threes are going to divide out so you'll be negative for is that greater than or equal to -8 + -4 is the negative X remember on the number line the negatives go backwards so you'd have one two three four negative four five six seven eight -8 -4 is bigger cuz it's more the right to this is true so yes -3 is a solution to this inequality

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