Question

find the sum 17x+5x - this was the correct problem lol im sorry people

Answer 1

there we go
now this is what you do
add 17 and 5 together, and stick an \(x\) next to it

Answer 2

since \(17+5=22\) we have
\[17x+5x=22x\]

Answer 3

thats it?

Answer 4

like 17 dollars and 5 dollars is 22 dollar

Answer 5

yeah, that's it

Answer 6

it is called combining like terms

Answer 7

just like adding apples to apples

Answer 8

woah :) cool beans... thanx satelite

Answer 9

yw
easy right?

Answer 10

yep but why coudlt u do it the previous one b4?

Answer 11

One of the ideas behind combining like terms is the distributive property:
a(b + c) = ab + ac

We can go backwards, take the a back out.
ab + ac = a(b + c)

In this case, we have 17x + 5x
We can take the x out, so it becomes x(17 + 5)
And by adding together the 17 and 5, we get 22. 22x.

In the previous example, we had an x^3 and an x.
If we try to take out an x in x^3 + 4x (not exactly the same as before, but same idea), we get "x(x^2 + 4)", and x^2 + 4 cannot add together.

Does that make sense?

Answer 12

If we did something like 3x^3 + 4x^3, we could take out the x^3 and it'd become
"x^3(3 + 4)", which becomes 7x^3

Answer 13

sort of ... im getting there... thanx for ur help guys

Answer 14

You're welcome. The way I'm explaining is a tad more technical than the more intuitive "combining like terms" idea.
The main idea with it all, though, is that you don't know what the variable represents, so you can't add together x and x^3. There's just no equality here that can tell us what x actually is.

Answer 15

Simple proof:
let x = 2
Then if it does indeed combine to 22x, then 17x+5x should give the same value of 22x when x is substituted:
\[22(x)=17(2)+5(2)\]
\[44 = 44\]

But let's say you thought you could combine x^2 and x.
\[17x+5x^2=22x?\]
\[17(2)+5(4)=22(2)\]
\[54 \neq44\]