SOLUTION: Hello My name is Aj and this is my problem: I must "Solve for given variable" (I presume they want me to solve for "x") (3x +4)/(x -2) = 5/6 The answer is " x = -(34/13) "

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Question 627732: Hello My name is Aj and this is my problem:
I must "Solve for given variable" (I presume they want me to solve for "x")
(3x +4)/(x -2) = 5/6 The answer is " x = -(34/13) "
THINGS I HAVE TRIED
Step 1 : (3x +4)/(x -2) = 5/6
vvvvvvvvvvvv
2x -2 = 5/6
(I divided the two set of numbers because I didn't know any other way of getting rid of the second variable.)
Step 2 : 2x -2 = 5/6
(add +2 to both sides to get rid of the "-2")
vvvvv vvv
2x = 17/6

Step 3 : (2x)/2 = (17/6)/2
vvvvvv vvvvvvvv
x = ?
(I don't even know how to go about finishing this. but whatever this answer would end up being, im pretty sure its not " x = -(34/13)" )
My question is,"What am I doing wrong, and How do I correctly solve for " x ". "
Thank you for you time and your assistance,
AJ.

Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given equation

Cross multiply

Distribute.

Subtract from both sides.

Subtract from both sides.

Combine like terms on the left side.

Combine like terms on the right side.

Divide both sides by to isolate .

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Answer:

So the solution is

So your answer is correct. However, there are a few issues in your steps (eg: you lost a negative sign somewhere, not sure where).

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Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

In general . And even so, how did you manage to come up with ?

What you need to do first is cross-multiply. In general, the process is the numerator on one side of the equals sign times the denominator on the other side is equal to the denominator on the first side times the numerator on the other side, thus:

To specifics:

Applying the cross-multiply process:

Distribute to remove parentheses:

I'll let you take it from here.

John

My calculator said it, I believe it, that settles it