How do you solve #6/5=2/(5n)#?

2 Answers
Feb 15, 2017

Answer:

#6/5 = 2/"5n" : n = 1/3 # (Decimal = 0.33333333333333333333............)

Explanation:

#6/5 * x/x = 2/"5n"#
Solve for #x#
# x = 2/6 = 0.33333333333333333......, 1/3#

#6/5 * 0.3333333/0.33333333 = 2/"5n"#

#5 * 0.333333333333333333..................... = 5n #

This means n = 0.3333333333333333333333......, #1/3#

Feb 15, 2017

Answer:

#n=1/3#

Explanation:

Multiply both sides of the equation by the #color(blue)"lowest common multiple"# (LCM) of the denominators 5 and 5n

the LCM of 5 and 5n is 5n

#cancel(5)^1 n xx6/cancel(5)^1=cancel(5n)xx2/cancel(5n)#

#rArr6n=2#

To solve for n, divide both sides by 6

#(cancel(6) n)/cancel(6)=2/6#

#rArrn=2/6=1/3#

#color(blue)"As a check"#

Substitute this value into the right side and if it equals the left side then it is the solution.

#"right side "=2/(5xx1/3)=2/(5/3)==2/1xx3/5=6/5#

#rArrn=1/3" is the solution"#