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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.