Identity property of 0

Evaluate 0 plus y plus -7 when y is equal to -3 and y is equal to 0 and y is equal to 7. So let's take the first situation where y is equal to -3... Then this expression right here would be... 0 plus -3 (because that's our "y" now) plus -7. Now 0 plus or minus anything won't change its value So you can really just ignore the 0 here. This is going to be the same thing, this is going to be the exact same thing, as -3 plus -7. -3 plus -7 Now we could draw a number line here, just to help us visualize it But even if we didn't have the number line, we could say "Look, we're already 3 below zero... We're going to go another 7 to the left... another 7 more negative." So we're 3 away from zero, we're going to go 7 more away from zero So we're going to be 10 to the left of zero, or -10. Or another way to think of it... Lemme draw the number line there (always better to have the visual). So we're starting (this is zero) We're starting at -3, and to that we're adding -7 So we're starting at -3, the absolute value is -3[sic] is our starting point. To that we're adding another negative 7 We're going to move another 7 to the left. So we're adding (let me draw this)... we're adding a negative 7 right over here We're adding a negative 7 right over here So what's the length of this over here? The absolute value of -7 is equal to 7... that's the length of this arrow. But we're moving it to the left. The abolsute value of this arrow right here (the absolute value of negative 3) is 3. So we're already 3 to the left, now we're moving 7 more to left So now we're going to be 10 to the left. We are going to be 10 to left. 10 to the left. This is literally, this is equal to the absolute value of -7... Let me do it in the order that we wrote it in the problem... So this is equal to the absolute value of -3 (you'd want to use the same colors) The absolute value of -3 plus the absolute value of -7. But we're to the left of zero (we've been moving to the left) so it's the <i>negative</i> of that which is -10 So if your signs are the same, you can just take the absolute value of them say "ok, that's how far we're going to move, total. and we're that far from zero to the left" So the answer here is -10 That was when y is -3. Let's think about when y is equal to 0. When y is equal to 0, this expression up here becomes 0 plus 0 (our y here is going to be zero)... (We'll do it in that same blue color.) .... plus 0 plus -7. Now, if you add 0 to anything it's not going to change the value. So this thing over here, this is pretty straight-forward, these don't matter It's just going to be equal to -7 Now let's do the last one (when y is equal to 7) It's going to be 0 plus (our y is equal to 7) so 0 plus 7 and then we have plus -7 Now there's a couple of ways to do this... You could literally just say "now adding a negative number is equivalent to subtracting the number". You could say this is equivalent to 0 plus 7 minus 7 Plus -7 is the same thing as subtracting a 7 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 So let's say that this is zero We're starting off at 7. We're 7 to the right of zero. And to that we're adding a -7. So we're going to move 7 to the left of where we were. 7 to the left of 7 which was 7 to the right of 0! This gets us back to 0. So the answer is... zero.