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# Substitution with negative numbers

## Thuyết minh video

let's give ourselves some practice substituting positive and negative values for variables so we're told to evaluate X might result to evaluate X minus negative Y where X is equal to negative 2 and y is equal to 5 so everywhere we see an X we could replace with the negative 2 everywhere we see a why we replaced with a 5 so this is the Y right over here and then of course and then of course this is an X so let's do that so instead of that X let's write negative 2 so we have negative 2 minus and then we have open parenthesis a negative why Y is equal to Y is equal to 5 now what is this going to evaluate to well this is the same thing as negative 2 now subtracting a negative 5 so all of this business here subtracting a negative 5 that's the same thing as adding a 5 it's going to be negative 2 plus 5 which is equal to 3 this is going to be equal to 3 and there's several ways to think about this on my brain things okay I'm starting at negative 2 if I add 2 I get to 0 and then I would have to add another and then I have to add another 3 so that gets me to 3 you could even view this as you could even view this my brain kind of says negative 2 well let's see I have to add I have to add 2 to get back to 0 and then I have to add another 3 if I want to add a total of 5 so this is going to be 0 plus 3 gets me to 3 another way to think about it negative 2 plus 5 is the same thing as 5 minus 2 5 minus 2 which is of course equal to 3 or you can of course draw it on a number line and you would say if you start at negative 2 and you take five steps to the right you get to positive 3 let's do another one of these this one's a little bit more a little bit more complex so let's see we're told to evaluate 3 minus negative 6 plus negative H plus negative 4 where H is equal to negative 7 well there's two ways you could do it I could just take the negative 7 and replace it H with that negative seven or I could actually try to simplify this expression first and then do the substitution for H so let's actually do that I my brain feels like doing that so this expression I have the three but instead of subtracting a negative six instead of subtracting a negative six that's going to be the same thing just adding 6 so 3 plus 6 and adding a negative H adding a negative H adding a negative H that's the same thing as just subtracting H so 3 plus 6 minus H and then adding a negative 4 adding a negative 4 that's the same thing as subtracting 4 that's the same thing as subtracting 4 and now of course we can do this in any we you know addition and subtraction we have we can we can change the order in which we do it so let's let's do that just to kind of simplify all of this so actually first of all I can figure out what 3 plus 6 is 3 plus 6 is equal to 9 and then I have this minus 4 here so I could say 9 minus 4 like she I want to be careful not to skip any steps so 3 plus 6 3 plus 6 in a color that you can see so 3 plus 6 is 9 so that's 9 minus H minus 4 minus 4 now I could I could change the order in which I do this addition or subtraction so this is going to be the equivalent of 9 minus 4 9 minus 4 minus H minus H and I just did that so I can simplify and figure out what 9 minus 4 is 9 minus 4 of course let me do some blue and navy blue 9 minus 4 is 5 so this whole thing simplifies to 5 minus H before I even did the substitution and now I can substitute H with negative 7 so this is going to be equal to this is going to be equal to when I do the substitution I'll write it up here it's going to be 5 minus under the minus of that magenta color - and now it's where I see an H I'm going to replace it with negative 7 five minus negative seven you want to be very careful that you might be simply zero I have a negative here negative here let me just replace H with the seven remember H is negative seven so you're subtracting H you're going to subtract negative seven this is 5 minus negative seven which is the same thing which is the same thing as 5 + 7 5 plus 7 which we all know is equal to 12 and we're done let's do a few more of these you can't you can't really get enough practice here this is some important foundational skills for the rest of your mathematical lives all right so consider I don't array it make it too stressed about it it's it at the following number line all right so we got a number line here and they let's see they didn't mark off all the numbers here this is negative 4 he is at this point this is then we go to 2 so it looks like we're counting by twos here that this is negative 2 this is 0 yep negative 4 if you increase by 2 negative 4 negative 2 0 2 4 this would be a 6 this would be a negative 6 they intentionally left those numbers off so we have to figure out that hey look between negative 4 & 2 that you have to to go from negative 4 to 2 if to increase by 6 and we only have 1 2 3 hash marks so each of those hash marks must be increasing by 2 well anyway now we know now we know what all the points on the number line are evaluate E - f well we know we know that E is equal to negative 2 and we know we know that F is equal to 4 so this is going to be the same thing e is equal to negative 2 - - positive 4 - positive 4 let me do that same blue color - 4 well negative 2 minus 4 we have the number line in front of us this is just going to be negative 6 if you start at negative 2 you subtract if you subtract 2 you get 2 negative 4 you subtract another 2 you get 2 negative 6 so we are done let's do one more of these let's evaluate t plus negative u or again tea and you are on this number line and it looks like each of these hash marks we're incrementing by three as we go up zero three six and if we go down zero negative three negative six so it's clear that U is equal to three U is equal to three and it is also clear that T is equal to negative six T is equal to negative six so T plus negative U is going to be so it's going to be negative six plus negative six plus negative u U is three U is three you want to be very careful you might say oh I'll use positive so I'm just gonna put a positive number here but remember it's negative you wherever see either you replace it with the three so it's negative three so this is going to be six plus negative three or starting negative six plus negative three which we can rewrite it as negative six minus three all of this business could be re-written as negative six minus 3 negative six minus three if you're at negative six and you go three to the left you go three more negative you're going to end up at negative nine and we're all done