We are asked to find the only whole-number solution to the inequality system:
11 < 3 x - 4
35 > 5 x + 2
Solving for x in both inequalities, we get:
11+ 4 < 3 x
15 < 3 x
15/3 < x
5 < x
and:
35 - 2 > 5 x
33 > 5 x
33/5 > x
6.6 > x
When we plot this inequality on the number line, we get the following image that shows clearly the only whole-number solution:
so, since 5 cannot be selected because the inequality asks for STRICTLY larger than 5, the only whole-number left is "6".
