Question

Let f(x)= –2x + 4 and g(x) = –6x – 7. Find f(x)– g(x).

Answer 1

Since we have to find f(x) - g(x)

Write it this way:

f(x) - g(x)
(–2x + 4) - (–6x – 7)

Simplify.

Answer 2

how do you simplify?

Answer 3

Add like terms.

Answer 4

can you show me?

Answer 5

what you would do is -2x+-6x to get? and 4+-7 to get? And you'll have your answer

Answer 6

wait what? i'm so confused..

Answer 7

-2x and -6x are like terms because of the X's so add those.. and 4 and -7 are alike as well because they don't have an X. Add those

Answer 8

How far did you get?
Do you understand this step

f(x) - g(x)= (–2x + 4) - (–6x – 7)

Answer 9

nope

Answer 10

The question is
f(x)= –2x + 4 and g(x) = –6x – 7. Find f(x)– g(x).

f(x) is short-hand for -2x+4 (think of it as a nickname)
g(x) is short-hand for –6x – 7

when someone wants f(x)-g(x) they want
(-2x+4)- (-5x-7)

we say
f(x) - g(x)= (–2x + 4) - (–6x – 7)

so there is not too much to understand, except that you can subtract complicated things like (-2x+4) and (-6x-7)

Answer 11

*typo in
when someone wants f(x)-g(x) they want
(-2x+4)- (-5x-7)
should be
(-2x+4)- (-6x-7)

Answer 12

clear as mud?

Answer 13

but you are not finished because you can simplify this

f(x) - g(x)= (–2x + 4) - (–6x – 7)

Answer 14

f(x) - g(x)= (–2x + 4) - (–6x – 7)
we should write this as
f(x) - g(x)= (–2x + 4) + -1* (–6x – 7)

(subtraction is the same as adding a negative number, and a negative number is -1 times that number)

the first step is "distribute" the minus one in
-1*(–6x – 7)

this is a "rule" you should learn: distribute means multiply the -1 times each term inside
can you do that?

Answer 15

i'll try..

Answer 16

so it's 2x +4 -6 -7?

Answer 17

Let's concentrate on
-1*(–6x – 7)
it is best to think of this as
-1* (-6*x + -7)

btw, remember that -6x means -6*x (-6 times x)

distribute the -1 means multiply -1 times each term inside the parens
-1* -6*x + -1*-7

now we can simplify this. what do we get ?

Answer 18

if it were -1*-6* 8 you could do it, right? what about doing it half-way:
-1*-6 is +6 so we get 6*8

if we had x instead it would be 6x
-1*-6*x is 6x

Answer 19

If you have time later, try some of these videos
http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/manipulating-expressions/v/combining-like-terms

Answer 20

okay so i's 6x+8?

Answer 21

almost. what is
-1*(–6x – 7) ?

Answer 22

I should write is as
-1*(–6x + –7)

Answer 23

6x+8

Answer 24

so you are saying -1*-7 is 8?

Answer 25

isn't it?

Answer 26

1+7 is 8
-1+ -7 is -8

by 1*7 is 7
and
-1* 7 is -7
and
1* -7 is -7
what is
-1* -7 ?

Answer 27

7?

Answer 28

yes. so what is
-1*(–6x + –7)

Answer 29

6x+7?

Answer 30

yes. so far we have
f(x) - g(x)= (–2x + 4) - (–6x – 7)
becomes
f(x) - g(x)= (–2x + 4) +6x+7

Answer 31

we do not need the parentheses, so we could write this as
f(x) - g(x)= –2x + 4 +6x+7

you know we can add numbers in any order so we could write this as
f(x) - g(x)= 6x + -2x +4 + 7

Answer 32

now you can do some of that, right? you can add 4 and 7 and put down one number instead of 4+7

Answer 33

8x+11?

Answer 34

the 11 is correct. 4+7 is 11

you should get used to writing the whole equation (good practice)
f(x) - g(x)= 6x + -2x +11

now for the x's you have 6 x's and take away 2 x's
how many x's do you have?

Answer 35

4

Answer 36

yes you have 4 x's we write that as 4x

so finally, what is
f(x) - g(x)= 6x + -2x +11

write down the whole equation

Answer 37

4x+11?

Answer 38

yes, but that isn't the whole equation.

Answer 39

so what is it?

Answer 40

you should write the left hand side, the = sign, and then the right-hand side

Answer 41

okay now i'm confused again

Answer 42

like this
f(x) - g(x)= 4x+11

Answer 43

oh okay, so that's my answer then?

Answer 44

yes

Answer 45

okay thank you for your help! :)