Sure! Let's go through the solution step-by-step.
We start with the inequality:
[tex]\[ -15 < 3n \leq 6 \][/tex]
First, we'll isolate [tex]\(n\)[/tex] by dividing all parts of the inequality by 3:
[tex]\[ \frac{-15}{3} < \frac{3n}{3} \leq \frac{6}{3} \][/tex]
This simplifies to:
[tex]\[ -5 < n \leq 2 \][/tex]
Next, we need to find the integer values for [tex]\(n\)[/tex] that satisfy this inequality. That means we need to identify all integer values between -5 and 2, inclusive of 2 and exclusive of -5.
So the integer values of [tex]\( n \)[/tex] are:
[tex]\[ -4, -3, -2, -1, 0, 1, 2 \][/tex]
Thus, the integer values of [tex]\( n \)[/tex] that satisfy the inequality [tex]\( -15 < 3n \leq 6 \)[/tex] are:
[tex]\[ \boxed{-4, -3, -2, -1, 0, 1, 2} \][/tex]
