Question

Solve please:
1/5n + 2/3 -2 = n - 2/5

Answer 1

`\boxed{n = 6}`

Explanation:

Given equation is:

`(1)/(5)n\:+\:(2)/(3)-2\:=\:n\:-(2)/(5)`

First let's get rid of the fractions by multiplying by 15 which is the LCM of 3 and 5 and is simply 3 x 5. The LCM of two prime numbers is the product of the primes

Multiplying throughout by 15:

`15\cdot (1)/(5)n\:+15 \cdot \:(2)/(3)- 15\cdot 2\:=\:15\cdot n\:-15\cdot (2)/(5)`

==>
`3n+10-30 = 15n - 6`

==>
`3n -20 = 15n - 6`

Move 3n to the right side(subtract 3n from both sides) and move -6 to the left side(same as adding -6 on both sides):

==>
`3n - 3n -20 + 6 = 15n - 3n - 6 + 6`

==>
`-14 = 12n\\`

Divide by 12:

`\implies n = (-14)/(12) = -(7)/(6) = -1.16666....`

Answer:

`\boxed{n = 6}`