algebra help needed?

Question

solve this rational inequality. its the one with the numberline you have to pick a random number to see if it works that one.

4 - 1/b < 3/b

Answer 1

These are easier to solve if you assume they are equal first: 4 - 1/b = 3/b. First add 1/b to both sides: 4 < 4/b

Then put a 1 under the single 4 and cross multiply: 4b = 4

Then divide by 4: b = 1

Note that if b = 0 the inequality is undefined. So, that is another boundary point. This leaves three intervals that could work:
b > 1
0 < b < 1
b < 0

Now you have to see which work so you pick a random number from each interval to try in the original. Say you pick 2, 0.5, and -1

First try 2: 4 - 1/2 < 3/2
3 1/2 which is 7/2 < 3/2 false

Now 0.5: 4 - 1/0.5 < 3/0.5

4 -2 < 6 true

Now -1: 4 - 1/-1 < 3/-1
4 + 1 < -3 false

That means that the only numbers that work are 0 < b < 1

Answer 2

would appear that since there is a fraction on the right -
and fractions are less than 1

this statement will always be false

idk