Solving equation..?

Here's the problem:



I'm suppose to be solving the equation but I'm not sure how to get started.

I think I multiply both sides by 5x + 6 right?

Which gives me 10x + 3 on the left side and 1/2(5x + 6) on the right

Then do I just distribute?

You will get all kinds of "quickie" ways to solve a proportion. The bottom line for most problems involving fractions is to multiply both sides of the equation by the least common denominator. That works for fractional equations, which a proportion is just a special case of. One quickie rule for solving a proportion is "the product of the means is equal to the product of the extremes." My advice is to stay away from those who advocate "just cross multiply" unless you figure out why you are doing so.

Example: 3/6 = 10/20 : 3*20 = 6*10

Just cross-multiply :wink:

And KillerNoodle, you must know what are the extraneous values for the variable you're solving for.
For instance, whatever values of the variable that make the denominator zero, must be rejected.

So here, after setting (5x + 6) = 0, you see that x = -6/5 is not allowed. If you get solutions that are
different from this value/these values, then you keep them. But if your only candidate solution at the end of
solving is/are this rejected values, then the answer would be "no solution."

No this is easy. Just cross multiply as Denis said.
So you get 2(10x+3) which is 20x+6 on one side.
Then you get 1(5x+6) which is the same 5x+6 on the other side
So you should have 20x+6=5x+6
Then just solve it as this:
Subtract 5x from both sides
Now you have:
15x+6=6
Now just subtract 6 from both sides and you should get 15x=0
So divide by 15 both sides and you should get x=0 since anything times 0 is 0.
Now if you plug it in to see if it is right you get
10(0)+3 1
----------- = -------
5(0)+6 2

Then

3 1
-- = --
6 2

THAT IS TRUE SO IT IS RIGHT

i hope i helped