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evaluate zero plus y plus negative seven when y is equal to negative three y is equal to zero and Y is equal to seven so let's take the first situation where Y is equal to negative three then this expression right here would be zero plus negative three because that's our Y now plus negative 3 plus negative seven plus negative seven now zero plus or minus anything won't change its value so you can really just ignore the zero here so this is going to be the same thing this is going to be the exact same thing as negative three negative three plus negative seven plus it's a different color plus negative seven negative three plus negative seven and now we can draw a number line here just to help us visualize it but even if you didn't have the number line you'd say look we're already three below zero we're going to go another seven to the left we're going to go another seven more negative so we're four three away from zero we're going to go seven more away from zero so we're going to be ten to the left of zero or a negative ten or another way to think about let me draw the number line they're always better to have a visual so we're starting so this is zero we're starting at negative three we're starting at negative three and to that we're adding negative seven so we're starting at negative three the absolute value is negative three at our starting point to that we're adding another negative seven we're going to move negative seven to the left so we're adding let me draw this we're adding a negative seven right over here we're adding a negative seven right over here so what's the length of this right over here the absolute value of negative seven is equal to 7 that's the length of this error but we're moving it to the left the length of this arrow right here the absolute value absolute value of negative three is three so we're already three to the left now we're moving seven more to the left so now we're going to be ten to the left we are going to be 10 10 to the left 10 to the left this is literally this is equal to the absolute value of negative seven this is let me do it in the order that we wrote in the problem so this is equal to the absolute value of negative three you want to use the same colors the absolute value of negative three plus the absolute value of negative seven plus the absolute value of negative seven negative seven but we're to the left we're to the left of zero we've been moving to the left so it's the negative of that which is negative ten so if your signs are the same you can just kind of you take the absolute values of them say okay that's how far we're going to move total and we're that far away from zero to the left since everything was a negative number so the answer here is negative ten so that was y is equal to negative three let's think about when Y is equal to zero when y is equal to zero this expression up here becomes zero plus zero our Y here is going to be zero let me do that in that same blue color plus zero plus negative seven plus negative seven now you add zero to anything it's not going to change the value so this thing right over here this is pretty straightforward these don't matter it's just going to be equal to a negative seven now let's do the last one when y is equal to seven so our expression is going to be zero plus our Y is equal to seven so zero plus seven and then we have a plus a negative 7 plus a negative seven now there's a couple of ways to do this you could literally just say well adding a negative number is equivalent to subtracting the number you could say this is equivalent to 0 plus seven minus seven plus negative seven is the same thing as subtracting a seven the zero doesn't matter so this is equal to 7 minus 7 which is equal to zero another way to think about it let's draw a number line let's draw a number line so let's say that this is zero we're starting off at seven so we're starting off at seven where seven we are seven to the right of zero and to that we are adding a negative seven so to that we're going to add a negative seven so we're going to move two seven to the left of where we were seven to the left of 7 which is 7 to the right of zero so this gets us back to zero over here so the answer is zero