How do I solve this inequality, 4x−7 < 12 and 3x + 5 > 11?

Question

My homework says to solve,

#6. 4x−7 < 12 and 3x + 5 > 11 in algebraic form.

Does this mean I solve each inequality separately and then combine both answers? If so I got: 2<x<19/4

Or do I combine them like this: 4x−7 < 12 + 3x + 5 > 11 with a addition sign, and solve it like that?

Answer 1

4x - 12 < 7 and 3x + 5 > 11

The word "and" means that both conditions must be met.

4x < 19 and 3x > 6

x < 19/4 and x > 2

Solution set: all real numbers between 2 and 19/4

2 < x < 19/4

Using interval notation, the solution set is (2, 19/4)