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CCSS.Math:

so we have two inequalities here the first one says that X plus 2 is less than or equal to 2x and this one over here in guess this light purple move color is 3 X plus 4 is greater than 5 X now over here we have four numbers and what I want to do in this video is test whether any of these four numbers satisfy either of these inequalities so I encourage you to pause this video and try these numbers out does zero satisfy this inequality does it satisfy this one does 1 satisfy this one does it satisfy that one so I encourage you to try these four numbers out on these two inequalities so assuming you have tried that so let's work through this together so let's say so if we try out if we try out zero on this inequality right over here let's substitute let's substitute X with zero so we'll have zero plus two needs to be less than or equal to two times zero is that true well on the left hand side the sieve is two needs to be less than or equal to zero is that true is 2 less than or equal to zero no 2 is larger than zero so this is not going to be true so this does not satisfy this does not satisfy the left hand side inequality let's see if it satisfies the right hand side inequality or this inequality right over here so we in order to satisfy three times zero plus four needs to be greater than five times zero well 3 times zero is just zero five times zero zero so for needs to be greater than zero which is true so it does it does satisfy they'll write this inequality right over here so zero is does satisfy this inequality now let's try out one let's try out one so to satisfy this one one plus two needs to be less than or equal to 2 C 1 plus 2 is 3 is 3 less than or equal to two no three is larger than do so this does not satisfy the left-hand inequality what about the right hand inequality right over here so 3 times 1 plus 4 needs to be greater than 5 times 1 so 3 times 1 is 3 plus 4 so 7 it needs to be greater than 5 well that's true so both 0 & 1 satisfy 3x plus 4 is greater than 5x neither of them satisfy X plus 2 is less than or equal to 2x now let's go to the 2 I know my it's getting a little bit unaligned but I'll just do it all in the same color so you can tell so let's try it 2 here so two plus two needs to be less than or equal to 2 times 2 so 4 needs to be less than or equal to 4 well 4 is equal to 4 and it just has to be less than or equal so this satisfies this satisfies the left this inequality what about the right what about this purple inequality let's see 3 times 2 plus 4 needs to be greater than 5 times 2 so 3 times 2 is 6 plus 4 is 10 needs to be greater than 10 10 is equal to 10 it's not greater than 10 so it does not satisfy it does not satisfy this inequality if this was a greater than or equal to then this would have been a greater than or equal to and it would have satisfied it but it's not 10 is not greater than 10 its greater it's it would satisfy greater than or equal to because 10 is equal to 10 so 2 satisfies the left hand 1 but not the right hand 1 all right let's try out 5 so 5 over here five plus two needs to be less than or equal to 2 times 5 once again everywhere we see an X we replace it with a 5 so 7 needs to be less than or equal to 10 which is absolutely true 7 is less than 10 so it satisfies less than or equal to so 5 satisfies this inequality and what you're probably noticing now is that an inequality can have many numbers that satisfy it in fact they often haven't they sometimes will have nothing that satisfies it and sometimes they might have an infinite number of numbers that satisfy it and you see that right over here we're testing out a few numbers and for this left one zero and one didn't work 2 & 5 did work now this right one zero and one worked two didn't work let's see what five does so in order for five to satisfy three times X now X is we're going to try out for five we're going to try X being five three times five plus four needs to be greater than five times five three times five is fifteen fifteen plus four is 19 19 is to be greater than 25 it is not so five does not satisfy this inequality right over here so anyway hopefully you found that fun