Question

2/3(x+2)-1/4(x-2)
Which is an equivalent expression to the one above?
(1) 11/12x + 22/12
(2) 11/12x + 10/12
(3) 5/12x + 10/12
(4) 5/12x + 22/12

Answer 1

I assume this is
\[ \frac{2}{3(x+2)} - \frac{1}{4(x-2)} \]

Answer 2

if so, multiply the first fraction by 4(x-2)/4(x-2) (and notice you are doing (a+b)(a-b)= a^2-b^2 )
multiply the 2nd fraction by 3(x+2)/3(x+2)

Answer 3

or is it
\[ \frac{2}{3}(x+2) - \frac{1}{4}(x-2) \]

Answer 4

Yes phi its the second one

Answer 5

\[2/3(x+2)-1/4(x-2)\]

Answer 6

then distribute the 2/3 (that means multiply 2/3 times x and times 2
do the same for -1/4
then you have to "combine" like terms
can you do that?

Answer 7

Ill try one minute please

Answer 8

Ill try one minute please

Answer 9

so 2/3x+1.33333-1/4x+0.25

Answer 10

yes, but I am guessing they want you to stick with fractions (this question is really about fractions)

so (2/3)x + 4/3 - (1/4)x + 2/4

notice that last term is 2/4 (or 1/2) not 0.25 (which means 1/4)

Answer 11

oh I see

Answer 12

now combine 2/3 of an x minus 1/4 of an x

the common denominator is 12

Answer 13

8/12 and 3/12

Answer 14

yes so you now have
(8/12) x - (3/12) x +4/3 - 2/4

Answer 15

you can now subtract 8/12 x - 3/12 x to get 5/12 x

Answer 16

Isnt it 8/12x+3/12x+4/3+1/2

Answer 17

Or no need to simplify the 2/4

Answer 18

Im confused because dont you have to add to get rid of the -3/12

Answer 19

Wait nevermind I not understand

Answer 20

don't lose track of your signs.

start at the beginning
(2/3)x + 4/3 - (1/4)x + 2/4

you changed the 2/3 to 8/12 and the 1/4 to 3/12 to get
(8/12)x + 4/3 - (3/12) x + 2/4

now "collect terms" meaning put the x terms next to each other. notice the -3/12 x is negative

Answer 21

So now we have (5/12) + (4/3) - (1/2)

Answer 22

so like combining them.. pretty much simplifying the expression

Answer 23

you mean
(5/12)x + (4/3) - (1/2)

don't leave out the x

now do the same for the numbers, use 12 for the common denominator (because all the answers seem to be using 12)

Answer 24

I have the x on my paper just that I forgot to type it

Answer 25

EDIT: (5/12x) + (16/12) - (6/12)

Answer 26

almost done...

Answer 27

(5/12x) + (10/12)?

Answer 28

yes. If you are rusty with fractions see
http://www.khanacademy.org/math/arithmetic/fractions
take a peak at some of the videos.

Answer 29

Yeah i am never rusty with fractions, all these acuity exams I need to improve with them

Answer 30

The acuity exams say thats what I need to improve in

Answer 31

Thank you so much for your help you have earned a fan

Answer 32

thanks.

Answer 33

Can you help my out with two more problems ill be posting them now