How do you solve #(2y-3)/5+(9y-9)/4 = 21#?

2 Answers
Mark D.
Jun 25, 2018

Get a common denominator

#[4(2y-3)]/(4xx5)+[5(9y-9)]/[5xx4]=21#

#[8y-12]/20+[45y-45]/20=21#

#[53y-57]/20=21#

Multiply both sides by 20

53y-57=420

add 57

53y=477

divide by 53

y=9

Meave60
Jun 25, 2018

#y=9#

Explanation:

Solve:

#(2y-3)/5+(9y-9)/4=21#

In order to add or subtract fractions, they must have the same denominator. The least common denominator (LCD) for #1,4,5# is #20#. If we multiply both sides of the equation by #20#, we can cancel the denominators.

#color(red)cancel(color(blue)(20))^4xx(2y-3)/color(red)cancel(color(black)(5))^1+color(red)cancel(color(blue)(20))^5xx(9y-9)/color(red)cancel(color(black)(4))^1=21xxcolor(blue)20#

Simplify.

#4(2y-3)+5(9y-9)=420#

Expand.

#8y-12+45y-45=420#

Simplify.

#53y-57=420#

Add #57# to both sides.

#53y=420+57#

Simplify.

#53y=477#

Divide both sides by #53#.

#y=477/53#

Reduce.

#y=9#

Related questions
Impact of this question
937 views around the world
You can reuse this answer
Creative Commons License