Question 153434: 18-2/11a=5/11a-19
Answer by sbarbagallo(4)   (Show Source):
You can put this solution on YOUR website! 18-(2)/(11a)=(5)/(11a)-19
Since 18 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 18 from both sides.
-(2)/(11a)=-18+(5)/(11a)-19
Simplify the right-hand side of the equation.
-(2)/(11a)=-(407a-5)/(11a)
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*11a=-(407a-5)*11a
Since a is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
-(407a-5)*11a=-2*11a
Multiply -1 by 11a to get -11a.
-11a(407a-5)=-2*11a
Multiply -2 by 11a to get -22a.
-11a(407a-5)=-22a
Multiply -11a by each term inside the parenthesis (407a-5).
(-11a(407a)-11a(-5))=-22a
Complete the multiplication of -11a by each term inside the parenthesis.
(-4477a^(2)+55a)=-22a
Remove the parenthesis around the expression -4477a^(2)+55a.
-4477a^(2)+55a=-22a
Since -22a contains the variable to solve for, move it to the left-hand side of the equation by adding 22a to both sides.
-4477a^(2)+55a+22a=0
Since 55a and 22a are like terms, add 22a to 55a to get 77a.
-4477a^(2)+77a=0
Multiply each term in the equation by -1.
-4477a^(2)*-1+77a*-1=0*-1
Simplify the left-hand side of the equation by multiplying out all the terms.
4477a^(2)-77a=0*-1
Multiply 0 by -1 to get 0.
4477a^(2)-77a=0
Factor out the GCF of 11a from each term in the polynomial.
11a(407a)+11a(-7)=0
Factor out the GCF of 11a from 4477a^(2)-77a.
11a(407a-7)=0
Set the single term factor on the left-hand side of the equation equal to 0.
11a=0
Divide each term in the equation by 11.
(11a)/(11)=(0)/(11)
Simplify the left-hand side of the equation by canceling the common terms.
a=(0)/(11)
0 divided by any number or variable is 0.
a=0
Set each of the factors of the left-hand side of the equation equal to 0.
407a-7=0
Since -7 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 7 to both sides.
407a=7
Divide each term in the equation by 407.
(407a)/(407)=(7)/(407)
Simplify the left-hand side of the equation by canceling the common terms.
a=(7)/(407)
The complete solution is the set of the individual solutions.
a=0,(7)/(407)
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