How do you solve for n in #(1/2)x-(2/3)=4x#?

1 Answer
Nov 20, 2017

Answer:

#x = -4/21#

Explanation:

Given
#(1/2)x−(2/3) = 4x#
Solve for #x#

1) Clear the first denominator by multiplying all the terms on both sides by 2 and letting the denominator cancel.
After you have multiplied and canceled, you will have this:
#x - (4/3) = 8x#

2) Clear the second fraction by multiplying all the terms on both sides by 3 and letting the denominator cancel.
After you have multiplied and canceled, you get this:
#3x - 4 = 24x#

3) Subtract #3x# from both sides to get all the #x# terms together
#- 4 = 21x#

4) Divide both sides by 21 to isolate #x#
#-4/21 = x# #larr# answer

Answer
#x = -4/21#
..................................

Check
Sub in #-4/21# in the place of #x# in the original equation

#(1/2)x−(2/3) = 4x#

#(1/2)(-4/21)−(2/3) = 4(-4/21)#

Cancel
#(1/(cancel2^1))(-cancel4^2/21)−(2/3) = 4(-4/21)#

Clear the parentheses by distributing the 4
#- 2/21- 2/3 = -16/21#

Rewrite with a common denominator
#- 2/21- 14/21 = -16/21#

Combine like terms
#- 16/21 = -16/21#
Check!