Posted by Courtney on .
1/3x + 5/6 = 2/9x  1/3
How do I solve this to get the answer?
For basic algebra you need to understand that we can add (or subtract) the same quantity from both sides without affecting the = sign. We can also multiply and divide (except by 0) both sides without affecting the = sign.
For this equation
1/3x + 5/6 = 2/9x  1/3 add 1/3x to both sides to get
5/6 = 2/9x  1/3  1/3x then add 1/3 to both sides to get
5/6 + 1/3 = 2/9x  1/3x
Now factor x from the right hand side to get
5/6 + 1/3 = x(2/9  1/3)
Then divide both sides by (2/9  1/3) to get
(5/6 + 1/3)/(2/9  1/3) = x
The rest is arithmetic and you should be able to do that.
There is a much easier way to do that.
You don't need to factor anything.
Just get the like quantities on the same side like so,
(5/6+1/3)=(2/9x1/3x) then
7/6=1/9x and solve from there.
Amanda, there are probably a dozen "equivalent" ways to do this problem. I was trying to explain the steps I was doing.
And yes, if we have 2/9x1/3x we would think of it as
x(2/91/3)
You simply combined the terms, so the distributive property was used implicitly. That's all. I didn't 'factor', I separated out the common term of two terms. This is just the reverse of the distributive property.
I see you caught your arithmetic error too. Good job.
I also see you didn't have any arithmetic error, excuse me.
Another poster had a typo, but they still had the correct answer.
Never mind
WHY rational expressions that are being added must have an LCD, but rational expressions that are being multiplied do not need to have an LCD.
solve for x if 4(2x3)+32=60
And now I see I did use the word factor. I probably shouldn't have used that term because it's typically reserved for polynomials. Oh well...
However when you combined the terms this is exactly what you did too.
1/3x2/9x=5/61/3
1/9x=7/6
x=7/6 * 9
x=10 1/2
1/3x2/9x=5/61/3
1/9x=7/6
5/61/3=5/62/6=3/6=1/2 not 7/6 so
x=9*1/2=9/2
Check my arithmetic
Do it like this,
2/9x1/3x=5/6+1/3
Do you see how I moved the like quantaties to the same side?
Trust me I am in Geometry and passed Algebra with flying colors.

Algerbra 1 
crysta,
(ab/6c)5