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?
0x<-5
x>-5
x>-1
OX<-1

Answer 1

x > -5

Explanation:

Two-fifths of one less than a number is less than three-fifths of one more than that number.

x - 1

Two-fifths of one less than a number is less than three-fifths of one more than that number.

(2/5)(x - 1)

Two-fifths of one less than a number is less than three-fifths of one more than that number.

(2/5)(x - 1) <

Two-fifths of one less than a number is less than three-fifths of one more than that number.

(2/5)(x - 1) < (x + 1)

Two-fifths of one less than a number is less than three-fifths of one more than that number.

(2/5)(x - 1) < (3/5)(x + 1)

Multiply both sides by 5.

2(x - 1) < 3(x + 1)

Distribute on both sides.

2x - 2 < 3x + 3

Subtract 3x from both sides.

-x - 2 < 3

Add 2 to both sides.

-x < 5

Divide both sides by -1.

x > - 5