3/4x -1/3 =5 What is x?

1 Answer
Nov 17, 2017

#x = (64)/(9)#

Explanation:

Solve for #x#
#(3/4)x - (1/3) = 5#

1) Start by clearing the first fraction by multiplying all the terms on both sides by 4 and letting that denominator cancel.
After you have multiplied and canceled, you will get this:
#3x - (4/3) = 20#

2) Next, clear the other fraction by multiplying all the terms on both sides by 3 and letting that denominator cancel.
After you have multiplied and canceled, you will have this:
#9x - 4 = 60#

3) Add 4 to both sides to isolate the #9x# term
#9x = 64#

4) Divide both sides by 9 to isolate #x#
#x = (64)/(9)# <-- answer
........................

Check

1) Sub in #(64)/(9)# for #x# in the original equation

#(3/4)x - (1/3) = 5#

#(3/4)((64)/(9))- (1/3) # should still equal 5

2) Reduce the fractions to lowest terms

#(cancel3^1/(cancel4^1))((cancel64^16)/(cancel9^3))- (1/3) #

#(16)/(3) - (1)/(3)#

3) Subtract the fractions.
They already have a common denominator.

#(15)/(3)#
This should still equal 5 after you change it to a whole number

4) 5 does equal 5
Check!