Question

A sports company conducted a road test of a new model of a geared bike. The test rider cycled (3x - 2) miles on a flat road, (x2 - 5) miles uphill, and (2x + 7) miles downhill. Which simplified expression is equivalent to the total distance, in miles, for which the bike was tested?

Answer 1

When you see the word "total" think "add everything together".

Answer 2

I'd add the equations together?

Answer 3

Those are expressions, not equations. Yes, add them together.\
((an equation as an "=" sign in it))

Answer 4

true true. haha okay so uh (3x - 2)+(x2 - 5)+(2x + 7)?
Would I combine like terms?

Answer 5

correct. When you type x2, do you mean
\[x^{2}\] Just want to make sure.

Answer 6

yea im sorry x^2

Answer 7

ok, so what do you get?

Answer 8

I would get 8 and 14 now uh theres the x^2? yea would
I add that in with 3x and 2x?

Answer 9

Leave the x^2 alone...it has no like terms
Add the 3x and 2x together...they are like terms
Add the -2 and the +7 together...they are like terms
Your answer will thus have 3 different terms
____ + ____ + ____

Answer 10

alright so 5x + 5 + x^2?

Answer 11

bingo! good job!

Answer 12

Remember, to be like terms they have to have exatly the same variables (letters)
like 5xy and 2xy, 4x^2 and 15x^2, 4zb^2 and 9zb^2

Answer 13

I got it i got it thank you (:

Answer 14

so then now i'd have to work it out yea? just add it up?

Answer 15

right. you got the answer: 5x + 5 + x^2
Usually math teacher like to put the x^2 term first like
x^2 + 5x + 5
but it doesn't really matter

Answer 16

so then it'd be 10x^3? cause theres an x by 5?

Answer 17

Remember x^2 really means {x times x}, so there are really 2 x's in the term "x^2".
So x^2 and 5x don't have the same number of x terms. To be like, they have to have the same letters AND the same number of letters.

Answer 18

Don't combine the x^2 and 5x, because they are not like terms. x^2 has more x's than the 5x.

Answer 19

alright so just think of it as xxx ahah x times x so then
back to the problem uh 10x thats what 5x and 5 would become
what would I do to the x^2? just add that in to 10x?

Answer 20

i don't know why you are continuing on like this? You finished this problem 15 minutes ago when you wrote 5x + 5 + x^2. That's the answer! You're done! You can't combine any of these 3 terms. When I talk about terms I am talking about the 5x ... the -5 and the x^2

Answer 21

Haha oh Im sorry damn I didnt finish it though cause thats not one of the answers thats why I keep goin on Im on my virtual school and uh yea

Answer 22

These are my choices

x2 - x

x2 + 5x

x2 - x + 14

x2 + 5x + 14

Answer 23

oops we messed up! er i messed up. sorry. we forgot about the -5.
the number term will be -2 -5 + 7 = 0 so there is no number term.
the answer is just x2 + 5x

Answer 24

Ah okay haha thank you man I appreciate it