How do you solve #a/(9a-2)=1/8#?

1 Answer
Apr 27, 2017

Answer:

See the entire solution process below:

Explanation:

First, multiply each side of the equation by #color(blue)(8)color(red)((9a - 2))# to eliminate the fractions while keeping the equation balanced. #color(blue)(8)color(red)((9a - 2))# is the Lowest Common Denominator of the two fractions:

#color(blue)(8)color(red)((9a - 2)) * a/(9a - 2) = color(blue)(8)color(red)((9a - 2)) * 1/8#

#color(blue)(8)cancel(color(red)((9a - 2))) * a/color(red)(cancel(color(black)((9a - 2)))) = cancel(color(blue)(8))color(red)((9a - 2)) * 1/color(blue)(cancel(color(black)(8)))#

#8a = 9a - 2#

Next, subtract #color(red)(9a)# from each side of the equation to isolate the #a# term while keeping the equation balanced:

#-color(red)(9a) + 8a = -color(red)(9a) + 9a - 2#

#(-color(red)(9) + 8)a = 0 - 2#

#-1a = -2#

Now, multiply each side of the equation by #color(red)(-1)# to solve for #a# while keeping the equation balanced:

#color(red)(-1) * -1a = color(red)(-1)* -2#

#1a = 2#

#a = 2#