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Solve for x: 4 over 5 x + 4 over 3 = 2x


x = __________________ Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar.


I think it's 11/9 but I'm not sure?

Verified Answer :

Close, it's actually 10/9 or 1 1/9
This one's a bit more work because it includes factoring.
4/5x + 4/3 = 2x

First simplify 4/5x 
4/5x= (4/5) (X/1)= 4x/5

4x/5 +4/3=2x

Move the terms with x to the left by  subtracting 2x from both side. This cancels out the 2x on the right and will cause the equation to temporarily equal 0.

4x/5 + (-2x) + 4/3=0

Simplify -2x as well and so it will be -2x/1

-2x/1 must have the common denominator of 5 and to get that, you must multiply.

4X/5 + (-2X/1) (5/5) +4/3=0

4x/5 + ((-2x)(5)/5) +4/3=0

Since 4x/5 and -2x(5)/5 have a common denominator (5), combine the numerators.

(4x -2x(5))/5 +4/3=0

You're going to have to factor 2x from both 4x -2x(5)
2x(2-1(5)) 
2x (-3)/5 

-6x/5 +4/3=0

You want to have x by itself and since 4/3 is the only fraction without a variable, subtract it so it will be on the opposite side.

-6x/5=-4/3

Multiply 5 on both sides so that the fraction with the variable is no longer a fraction. 

-6x=-20/3

Multiply -1/6 from both side to get the answer of x.

-6x/-6= -20/3 (-1/6)

-1/6 cancels out -6 allowing x to be by itself. In order to get x by itself, factor 6 from -6

-6x/ -6 
- 6x/ 6(-1)  Cancel out the common factors (6)

-x/-1 You must rewrite the equation

- (-1) x= x

x=-20/3 (-1/6)

Multiply and then simplify the answer by finding the common factor which is 2.

x=20/18= 10/9

x=10/9 which is an improper fraction. 

The mixed number will be 1 1/9

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