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# Writing expressions with variables & parentheses

Video transcript

First consider the
expression for negative 5 plus the quantity of 4 times x. Now, take the product of
negative 8 and that expression and then add 6. So let's do it step by step. First, we're going to have
this expression-- negative 5 plus something. So it's going to be negative 5
plus the quantity of 4 times x. Well, that's just
going to be 4x. So it's going to be
negative 5 plus 4x. So that's this
expression up here. Now, take the product
of negative 8, so were going to
just take negative 8, and we're going to multiply
the product of negative 8 and that expression. So we're going to
take negative 8 and multiply it
so that expression is this thing right over here. So if we say the product of
negative 8 in that expression is going to be negative
8 times that expression, that expression is negative 5
plus 4x, so that's negative 8. That's that expression. The product of the two, so
we could put a multiplication sign there, or we could
just leave that out and implicitly it would
mean multiplication, take the product of negative
8 and that expression and then add 6. So that would be then
adding 6 right over here. So we could write it as negative
8 open parentheses negative 5 plus 4x and then add 6. Let's do one more. First, consider the expression
the sum of 7 and-- so that's going to be
7 plus something-- and the product of
negative 2 and x. The product of negative
2 and x is negative 2x. So it's 7 plus negative 2x. We could write
that as 7 minus 2x. So this is equal to 7 minus 2x. These are the same expression. What expression would be 4 plus? So now we're saying
4 plus the quantity of 2 times that expression? So it's going to be
4 plus some quantity. I'll put that in parentheses. The quantity of 2
times-- I'll do this in magenta or in yellow. 2 times that expression--
let me do this in blue-- that expression is this
thing right over here. So 4 plus the quantity of 2
times that expression, 2 times 7 minus 2x. And we are done.