Question

How many integers are common to the solution sets of both inequalities?

x+7 ≥ 3x
3x+4 ≤ 5x

Answer 1

first one:

x+7 ≥ 3x
-2x ≥ -7
x ≤ 7/2
x ≤ 3.5

2nd one:
3x + 4 ≤ 5x
-2x ≤ -4
x≥ 2

so "common" implies belonging to first AND the second, or

2 ≤ x ≤ 3.5

which for integers would be {2,3}