Question 153392: 2/5x+1/6=3/10x+1/3 solve for x
Answer by sbarbagallo(4)   (Show Source):
You can put this solution on YOUR website! (2)/(5x)+(1)/(6)=(3)/(10x)+(1)/(3)
Since (1)/(6) does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting (1)/(6) from both sides.
(2)/(5x)=-(1)/(6)+(3)/(10x)+(1)/(3)
Simplify the right-hand side of the equation.
(2)/(5x)=(5x+9)/(30x)
Since there is one rational expression on each side of the equation, this can be solved as a ratio. For example, (A)/(B)=(C)/(D) is equivalent to A*D=B*C.
2*30x=(5x+9)*5x
Since x is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
(5x+9)*5x=2*30x
Multiply (5x+9) by 5x to get 5x(5x+9).
5x(5x+9)=2*30x
Multiply 2 by 30x to get 60x.
5x(5x+9)=60x
Multiply 5x by each term inside the parenthesis (5x+9).
(5x(5x)+5x(9))=60x
Complete the multiplication of 5x by each term inside the parenthesis.
(25x^(2)+45x)=60x
Remove the parenthesis around the expression 25x^(2)+45x.
25x^(2)+45x=60x
Since 60x contains the variable to solve for, move it to the left-hand side of the equation by subtracting 60x from both sides.
25x^(2)+45x-60x=0
Since 45x and -60x are like terms, add -60x to 45x to get -15x.
25x^(2)-15x=0
Factor out the GCF of 5x from each term in the polynomial.
5x(5x)+5x(-3)=0
Factor out the GCF of 5x from 25x^(2)-15x.
5x(5x-3)=0
Set the single term factor on the left-hand side of the equation equal to 0.
5x=0
Divide each term in the equation by 5.
(5x)/(5)=(0)/(5)
Simplify the left-hand side of the equation by canceling the common terms.
x=(0)/(5)
0 divided by any number or variable is 0.
x=0
Set each of the factors of the left-hand side of the equation equal to 0.
5x-3=0
Since -3 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 3 to both sides.
5x=3
Divide each term in the equation by 5.
(5x)/(5)=(3)/(5)
Simplify the left-hand side of the equation by canceling the common terms.
x=(3)/(5)
The complete solution is the set of the individual solutions.
x=0,(3)/(5)
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