Question

Two-fifths of one less than a number is less than three-fifths of one more than that number. What numbers are in the solution set of this problem?

Answer 1

See the attachment..Hope it helps :-)

Answer 2

Numbers in the solution set of this problem = ( -5, ∞)

Explanation:

Let the number be x.

Two-fifths of one less than a number
`=(2)/(5)(x-1)`

Three-fifths of one more than a number
`=(3)/(5)(x+1)`

We have two-fifths of one less than a number is less than three-fifths of one more than that number

That is

`(2)/(5)(x-1)<(3)/(5)(x+1)\\\\(2)/(5)x-(2)/(5)<(3)/(5)x+(3)/(5)\\\\(x)/(5)+1>0\\\\x>-5`

Numbers in the solution set of this problem = ( -5, ∞)