Question

(2x+3) / 4 - (3x-5) / 3 = 2

solve for x.

Answer 1

First thing I would do is get rid of those denominators. You can get rid of something in the denominator my multiplying everything by that same number. So for example, if I wanted to get rid of that 4 in your first denominator, I would simply multiply everything by 4:
\[\frac{ 4(2x+3) }{ 4 }-\frac{ 4(3x-5) }{ 3 }=(2)(4)\]Note how I multiplied every term by 4. You must make sure everything gets multipliedif you do this. Now those 4's on that left fraction will cancel out and I will have this:
\[(2x+3)-\frac{ 4(3x-5) }{ 3 }=8\]
Also note how I keep thoseparenthesis. It's a very good habit to have, it'll help make sure you do not get the wrong signs or forget to do some sort of operation. Now I have that 3 left in the 2nd denominator. I can eliminate that in the same method I did with the 4, by multiplyong every by 3 like so:
\[3(2x+3) - \frac{ (3)(4)(3x-5) }{ 3 }=(8)(3)\]Again, I was careful to multiply everything by 3. Also notice how I just leave a bunch of things grouped together, but not actually multiplied out. This is also sometimes a good strategy. It lets you visualize what you're doing better in case you miss something or need to backtrack.
Now, I can cancel out that 3 in the second denominator, which will leave me with this.
\[3(2x+3)-4(3x-5)=24\]
That was probably the trickiest part of this problem. I'll leave it to you to see if you can finish the rest from here : )

Answer 2

but we have to do it this way for the test: can you show me where i am going wrong?\[\frac{ 2x+3 }{ 4} - \frac{ 3x-5 }{ 3 } = 2\]

Answer 3

then do this: \[\frac{ 3(2x+4) }{ 12 } - \frac{ 4(3x-5) }{ 12 } = 2\]

Answer 4

then: \[\frac{ 6x+12 - 12x - 2x +20 }{ 12 }\]

Answer 5

where am i going wrong??

Answer 6

@daftkillz - where did u get the "-2x" term in this equation ??

Answer 7

sorry delete that

Answer 8

typo

Answer 9

pretend its not there

Answer 10

its still wrong -_-

Answer 11

also
it should be 3(2x+3)

Answer 12

your error is in distributing 3(2x + 3)

you have 6x + 12..... which isn't correct

Answer 13

so it should be: 6x+9 - 12x +20 = 2

Answer 14

because thats still wrong..

Answer 15

RHS should be 12*2=24 right ?

Answer 16

wait what?

Answer 17

well if you change the 2 to 24... multiply every term by 12

you can solve your equation

Answer 18

wow made a stupid as mistake ok i get it now

Answer 19

i forgot 2 multiply the rhs by 12

Answer 20

thanks

Answer 21

Amy is twice as old as lucy. Three years from now the sum of their ages will be 42. how old is amy?

Answer 22

how do you do this?

Answer 23

can u share the equations u wrote for this problem ?

Answer 24

i did this:

Let lucy= L
and amy= A

3L + 3 = 42

3L = 39

2L = 26

therefore amy = 26


but the answer is 24

Answer 25

???

Answer 26

do it one by one... also you forgot to add three years to lucy's or amy's age :P

Answer 27

thts all

Answer 28

ohhh ok thanks :D