Question

two fifths of one less than a number is less than three fifths of one more than that number. what numbers are in solution set of this problema. x<-5b. x>-5c. x>-1d. x<-1

Answer 1

The best way to solve this is to do this step by step.
Let x = the number

Identify the word problem of the inequality.
Two fifths of one less than a number
= 2/5 (x-1)

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

Solve the inequality
2/5 (x-1) < 3/5 (x+1)
2x/5 - 2/5 < 3x/5 +3/5
-2/5 -3/5 < 3x/5 - 2x/5
-1< x/5
-5 < x
or
x > -5

The final solution set is B. x > -5