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?

1) x<-5
2)x>-5
3)x>-1
4)x<-1

Answer 1

(2/5)(x-1)<(3/5)(x+1) perform indicated multiplications

(2x-2)/5<(3x+3)/5 multiply both sides by 5

2x-2<3x+3 add 2 to both sides

2x<3x+5 subtract 3x from both sides

-x<5 divide both sides by -1 (remember to reverse direction of inequality sign when multiplying/dividing by a negative value)

x>-5