Question 248625
If we take {{{a < b}}} and add 3b to each side we get:
{{{a + 3b < b + 3b}}}
or
{{{a + 3b < 4b}}}<br>
The reason we did this is that the left side above now matches the right side of the other inequality:
{{{ab <= a + 3b}}}
Since {{{ab <= a + 3b}}} and {{{a + 3b < 4b}}} then
{{{ab < 4b}}}
by the transitive property.<br>
This inequality we can solve. We can divide both sides by b (without having to be concerned about reversing the inequality because we know that b is positive):
{{{a < 4}}}
Between this and the fact that a is also positive, the possible values for a are:
1, 2 and 3.