Question

What is the solution to the inequality -6+ [2p+3] less than 7?

Answer 1

If [2p+3] means the absolute value |2p+3|:

-6 + |2p+3| < 7
|2p+3| < 13
-13 < 2p+3 < 13
-16 < 2p < 10
-8 < p < 5

So the solution is (-8, 5).

If [2p+3] was intended as the floor (greatest integer) ⌊2p+3⌋, then
⌊2p+3⌋ < 13 ⇒ 2p+3 < 13 ⇒ p < 5,
so the solution would be p < 5.