6 th Grade Chapter 8 Lesson 6 Write and Graph Inequalities

hello welcome to chapter eight lesson six we're going to write and graph inequalities so two headings we'll be working on is right inequalities and we are also going to graph an inequality so the real world link says look at the situations below circle the numbers that are the possible answers in each situation jessica spent more than five dollars at the arcade so these are the numbers that indicate that she spent more than five dollars at the arcade so it could be any of these answers number two less than six people rang the bell on the mallet game so less than six people these are the numbers are less than six number three there were less than ten people nine for the ferris wheel so it could be any number less than ten number four it costs more than six tokens to write the bumper cards so it could be anywhere from seven to fifteen number five there are less than eight lemonade stands so we have all the numbers less than eight six there are more than 12 different flavors of taffy so we're gonna do those describe any pattern you see in exercises one through six so one pattern noticed was always circled the number that was next to the number in the problem so all these numbers are the same and always circle the number next to it so circled all the numbers on either side of the given number so we're going to write inequalities you can write an inequality to represent situation so example one write an inequality for each sentence you must be over 12 years old to ride the go cards so if must be over 12 years old so know my age needs to be greater than 12 in order to ride the co carts pony is less than fourteen and two tenths hands tall so pony is less than fourteen and two tenths number three you must be at least 16 years old to have driver's license so my age have to be 16 years old or older so have to be greater than or equal to 16. so can be 16 years old or older so go ahead and try and i'm actually going to do this with you after reading this so have to be my age has to be greater than 13 to play in the basketball league for use to use one stamp your domestic letter must weigh under three and half ounces so my stamp or should say the weight of my letter needs to be under so less than three and half ounces you must be over 48 inches tall to ride the roller coaster so my height has to be greater than 48 inches for you must be at least 18 years old to vote so that means can be 18 years old to vote could be 18 or older so have to be greater than or equal to 18. so now we're going to talk about graphing the inequalities and i'm going to show you some secrets in graphing these so we're going to start off with example 4. graphing each inequality on number line so i'm going to make little chart over here if am doing greater than or less than when graph use open circle okay there is nothing inside my circle if i'm doing greater than or equal to like an example five or less than or equal to when graph my circle must be closed so it must be filled in these are the two main things you you're going to need to remember just know whenever draw the line underneath close the circle so in example 4 it says graph is greater than 9. so i'm going to put an open circle at and then use my inequality to determine which way need to graph in order to graph this since my inequality is greater than it is if make an arrow out of that sign it is pointing to the right so i'm going to bold i'm going to highlight everything to the right of 9 and put an arrow and then have an open circle so i'm going to explain this one more time so have is greater than 9. now this is just greater than so when go to the 9 i'm going to have an open circle now need to graph everything since it's greater than this is my greater than symbol and if have to make it if make an arrow out of the greater than it points to the right so i'm going to i'm gonna bold everything on the right side of my nine and this is me graphing my inequality so nine and then everything to the right of nine so that means any number to the right of can will work will be solution for my inequality so if do number 5 since it is closed circle it is less than or or equal to that means my could be 10 or anything less than 10. so i'm going to highlight everything on the left side and remember with the less than symbol if make an arrow it points to the left but any in any of these numbers can be my solution so go ahead and try and all right so for we have is less than 15. since this is only less than i'm gonna have an open circle and less than symbol if make an arrow out of it i'm going to color in everything to the left of 15. so any one of these numbers can be solution for for my inequality for is greater than or equal to seven so i'm gonna go to my seven i'm gonna use closed circle and if have greater than symbol it's pointing to the right so i'm going to color everything to the right of it so any of these numbers to the right of 7 or 7 will be solution for my inequality so example 6 traffic on residential street can travel at speeds of no more than 25 miles per hour write and graph an inequality to describe the possible speeds so in residential street can do 25 miles per hour so know that it's going to have the or equal to sign so my speed has to be less than or equal to 25. so get 25 on my number line and do closed circle and highlight all my numbers that are less than 25 miles per hour but that is the end of the video so thank you for watching