Question

(3/5)x-(1/10)x=x-(7/2)

Answer 1

step 1)
to get rid of the fractions multiply everything by 10
show me what you get after that

Answer 2

why by 10 tho?

Answer 3

x=7

Answer 4

because it is the greatest common denominator between 5,10, and 2

Answer 5

do the same as we did in previous prob

Answer 6

im soo confused :(

Answer 7

i.e. all of the denominators can be factored
2=2
5=5
10=2*5
so 10 will wipe out all the fractions, try it and see!

Answer 8

i dont understand fractions!

Answer 9

can you multiply (1/2) by 10?

Answer 10

do i put it like this? (1/2) * (10/1)?

Answer 11

if you want, sure
so what does that simplify to?

Answer 12

5?

Answer 13

\[{1\over2}\times{10\over1}={10\over2}=5\]yes!
now do that to all the fractions, what do you have?

Answer 14

okay to 3/5 * 10 = 6
1/10*10/1=1

Answer 15

*so

Answer 16

7/2*10/1=35/1??

Answer 17

did i do it right?

Answer 18

good so far
but don't bother writing the "over one" that is unnecessary, all numbers are over one, so
7/2*10/1=35
so what do you have now after simplifying\[10*{3\over5}x-10*{1\over10}x=10x-10*{7\over2}\]?

Answer 19

yes you have done right so far :)

Answer 20

ok, what do i do next?

Answer 21

let's keep in mind what we are doing: we multiplied both sides of

(3/5)x-(1/10)x=x-(7/2) by 10 and got

10[(3/5)x-(1/10)x]=10[x-(7/2)]

which after simplifying the fractions gives

6x-x=10x-35

good so far?

Answer 22

yesss

Answer 23

good :)
so now we simplify by "combining like terms" (i.e. combine x's with x's, and pure numbers with pure numbers)
the first thing we can simplify is the left side
6x-x=?
you tell me...

Answer 24

is it just 6?

Answer 25

no,
combining like terms works like this:
3x+5x=(3+5)x=8x
12x-3x=(12-3)x=9x
so try again, what is
6x-x=?

Answer 26

but the other X has no number with it?

Answer 27

unless its 5x?

Answer 28

Yes! exactly!
all numbers can be thought of as having an invisible one multiplying it because 1x=x

so now we have

5x=10x-35

the next step is to get all the x's on one side and all the numbers without x's on the other side of the equals sign, any idea how to do that?

Answer 29

do i need to subrtracts 5x-5x and 5x-10x?

Answer 30

close.... you need to subtract 5x from both sides which gives
5x-5x=10x-5x-35
(you wrote above 5x-10x, so that is wrong because it is backwards)
so what does the above simplify to?

Answer 31

5x-35?

Answer 32

is the answer 7? lol

Answer 33

yes! good job.
just be sure to write out the steps properly though, you need to write BOTH SIDES of the equation
0=5x-35
35=5x
x=7
congrads =)

Answer 34

YAY!!! hahah >:)