SOLUTION: Solve: 4-(1/b)<3/b. Thank you

Question 42124: Solve: 4-(1/b)<3/b.
Thank you
Found 2 solutions by ind_blade, fractalier:
Answer by ind_blade(2) (Show Source): You can put this solution on YOUR website!
4-(1/b)<3/b
Multiply everything by "b" to cancel out the fractions so you will get
4b - 1 < 3
Add 1 to both sides
4b < 4
divide by 4 on both sides
b < 1
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
Previously the solution was listed as
4-(1/b)<3/b
Multiply everything by "b" to cancel out the fractions so you will get
4b - 1 < 3
Add 1 to both sides
4b < 4
divide by 4 on both sides
b < 1
---BUT---
realize that if b < 0 then the inequality needs to be reversed in step one...
Also realize that any b less than zero does not work...
You are better off adding 1/b to both sides first, and get
4 - (1/b) < 3/b
4 < 4/b
now divide by 4 and get
1 < 1/b or
1/b > 1
so that b < 1 but also b > 0 so that the full solution is
0 < b < 1
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