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Worked example: evaluating expressions using structure (more examples)

Video transcript
Let's do a few more examples where we're evaluating expressions with unknown variables. So this first one we're told 3x plus 3y plus 3z is equal to 1, and then we're asked what's 12x plus 12y plus 12z equal to? And I'll give you a few moments to think about that. Well let's rewrite this second expression by factoring out the 12, so we get 12 times x plus y plus z. That's this second expression here, and you can verify that by distributing the 12. You'll get exactly this right up here. Now, what is 12 times x plus y plus z? Well, we don't know yet exactly what x plus y plus z is equal to, but this first equation might help us. This first equation, we can rewrite this left-hand side by factoring out the 3, so we could rewrite this as 3 times x plus y plus z is equal to 1. All I did is I factored the 3 out on the left-hand side. And then if I want to solve for x plus y plus z, I just divide both sides of this equation by 3, and I'm left with x plus y plus z is equal to 1/3, and so here, instead of x plus y plus z, I can write 1/3. So this whole thing simplified to 12 times 1/3. 12 times 1/3 is the same thing as 12 divided by 3, which is equal to 4. Let's try one more. So here we are told that 3a plus 5b is equal to 2, and then we're asked what's 15a plus 15b going to be equal to? So we might-- let's see. I'll give you a few moments to try to tackle this on your own. Let's see how we might do it. We could approach it the way we've approached the last few problems, trying to rewrite the second expression. We could rewrite it as 15 times a plus b, and so we just have to figure out what a plus b is, and we'll be able to evaluate this expression. And so, it's tempting to look up here, and say maybe we can solve for a plus b somehow, but we really can't. If we divide-- if we try to factor out a 3, we'll get 3 times a plus 5/3b, so this doesn't really simplify things in terms of a plus b. If we try to factor out a 5, we'd get 5 times 3/5a plus b is equal to 2, but neither of these gets us in a form where we can then solve for a plus b. So in this situation, we actually do not have enough information to solve this problem. So it's a little bit of a trick. Not enough info to solve. Anyway, hopefully you enjoyed that.