How do you solve #\frac { 9} { x + 5} + \frac { 5} { 2} = 4#?

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Answer 1 · 2017-07-15T04:21:57

#x=1#

#9/(x+5) + 5/2 = 4#

minus #5/2# on both sides

#9/(x+5) = 3/2#

multiply by #x=5# on both sides

#cancel(x+5) xx 9/cancel((x+5)) = 3/2 xx (x+5)#

#9 = (3x+15)/2#

#2 xx 9 = (3(x+5))/cancel2 xx cancel2#

#18 = 3(x+5)#

#18/3 = (cancel3(x+5))/cancel3#

#6=x+5#

minus #5# on both sides

#1=x#

#color(black)(..................)#

Let's check our work

#9/(x+5) + 5/2 = 4#

#9/(1+5) + 5/2 = 4#

#9/6 + 5/2 = 4#

#3/2 + 5/2 = 4#

#8/2 = 4#

#4 = 4#

We were right! #x=1#