(x/(a-3)) = ax +5

Question

(x/(a-3)) = ax +5

mathstudent55 · Answer

You have one equation with 2 variables.
What are you asked to do?

sphott51 · Answer

solve for x

mathstudent55 · Answer

Ok

mathstudent55 · Answer

$\large \dfrac{x}{a - 3} = ax + 5$

mathstudent55 · Answer

The first step is to get rid of the denominator on the left side.
To do that, multiply both sides by a - 3.

mathstudent55 · Answer

Have you tried multiplying both sides by a - 3?
What did you get?

sphott51 · Answer

Do I distribute?

sphott51 · Answer

I'm confused about the fraction part

mathstudent55 · Answer

Yes. You multiply both sides by a - 3.
On the left side, it cancels out the denominator, and you have just x.
On the right side, you must multiply 2 binomials. You can use FOIL, for example.

mathstudent55 · Answer

$\large (\cancel{a - 3}) \times \dfrac{x}{\cancel{a - 3}} = (ax + 5) \times (a - 3)$

$\large x = (ax + 5)(a - 3)$

mathstudent55 · Answer

Do you understand it so far?

sphott51 · Answer

Yes, you said I foil the right side, right?

mathstudent55 · Answer

Yes, do that now.

sphott51 · Answer

Well, I think its a^2 x +5a - 3ax - 15 .. ?

mathstudent55 · Answer

Correct.

mathstudent55 · Answer

Now we have this

$\large x = a^2x + 5a -3ax - 15$

There are no like terms on the right side.

We need all terms with x on the left side,
so now we move the terms with x over to the left side.
That means subtract a^2x from both sides, and add 3ax to both sides.

sphott51 · Answer

x-a^2 x +3ax = 5a -15

mathstudent55 · Answer

Great.
Now factor out x from the three terms on the left side.

sphott51 · Answer

x( -a^2 +3a) = 5a - 15

mathstudent55 · Answer

You made a mistake.
I'll explain to you the mistake.
Before factoring, you started with 3 terms on the left side.
When you factor out the x, you must end up with something in the parentheses that when you multiply the x by it, you will again end up with the original 3 terms you had.
Notice what you have now.
You have x outside the parentheses, multiplied by only 2 terms in the parentheses.
There is no way you can multiply x by a binomial and end up with 3 terms.

mathstudent55 · Answer

In the parentheses, the first term is x.
When you factor x out of x, you must end up with 1 in the parentheses.

sphott51 · Answer

Sorry I do not know what you mean

mathstudent55 · Answer

$\large x - a^2x +3ax = 5a - 15$

$\large x(1 - a^2 +3a) = 5a - 15$

You see the first term in the parentheses? 
It is 1. That 1 is needed there, so that the parentheses still has 3 terms inside.
Factoring a common term is the opposite of applying the distributive property.
To undo the factoring of x you just did, you must be able to distribute the x you just factored out and end up with the same 3 terms.
The only way that is possible is if you have 3 terms in the parentheses after the factoring of x.

sphott51 · Answer

Ohh okay I see now

mathstudent55 · Answer

Ok.
Now you have the left side with a factored x and three terms inside the parentheses, like this

$\large x(1 - a^2 +3a) = 5a - 15$

Now there is only one step left.

x is being multiplied by that quantity in parentheses, and you want x alone, so divide both sides by the quantity int he parentheses.

mathstudent55 · Answer

Did you get a final answer?

sphott51 · Answer

x = 5a-15 / 1 -a^2 +3

sphott51 · Answer

Oh sorry, I didn't see as I was typing down

mathstudent55 · Answer

You are almost correct, but when you write everything in 1 line, you need to use parentheses to show that the numerator and denominator are quantities. Also, remember the last term of the denominator is 3a, not just 3. 

x = (5a - 15)/(1 - a^2 + 3a) 

This is what it looks like a fraction using more than 1 line of text. 

$\large x = \dfrac{ 5a - 15}{ 1 - a^2 +3a}$