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?

x<-5
x>-5
x<-1
x>-1

Answer 1

2/5 * (n - 1) < 3/5 * (n + 1)
2/5 * n - 2/5 < 3/5 * n + 3/5
- 2/5 - 3/5 < 3/5 * n - 2/5 * n
- 5/5 < 1/5 * n
- 1 < 1/5 * n /*5
- 5 < n
n > - 5

n = x

The correct result would be B) x > - 5.

Answer 2

Answer: The correct option is (B) x > -5.

Step-by-step explanation: Given that two-fifths of one less than a number is less than three-fifths of one more than that number.

We are to find the numbers that are in the solution set of this problem.

Let, 'x' represents a number in the solution set.

Then, according to the given information, we have

`(2)/(5)* (x-1)<(3)/(5)* (x+1)\\\\\\\Rightarrow 2(x-1)<3(x+1)\\\\\Rightarrow 2x-2<3x+3\\\\\Rightarrow 2x-3x<3+2\\\\\Rightarrow -x<5\\\\\Rightarrow x>-5.`

Thus, the solution set is represented by the number 'x' such that

x > -5.

Option (B) is correct.