2) To solve the inequality \( -14 \leq -5 + v \leq -4 \), we need to isolate the variable \( v \).
First, let's solve the left-hand side inequality \( -14 \leq -5 + v \):
\[ -14 \leq -5 + v \]
To isolate \( v \), we can add 5 to both sides of the inequality:
\[ -14 + 5 \leq -5 + v + 5 \]
\[ -9 \leq v \]
So, we have found the lower bound for \( v \): \( v \geq -9 \).
Now, let's solve the right-hand side inequality \( -5 + v \leq -4 \):
\[ -5 + v \leq -4 \]
To isolate \( v \), we can subtract 5 from both sides of the inequality:
\[ -5 - 5 + v \leq -4 - 5 \]
\[ v \leq -9 \]
So, we have found the upper bound for \( v \): \( v \leq -9 \).
Combining the lower and upper bounds, we have:
\[ -9 \leq v \leq -9 \]
Therefore, the solution is \( v = -9 \).
4) To solve the inequality \( m - 6 > 3 \) or \( m - 6 < -16 \), we need to find the values of \( m \) that satisfy either of the inequalities.
First, let's solve the first inequality \( m - 6 > 3 \):
\[ m - 6 > 3 \]
To isolate \( m \), we can add 6 to both sides of the inequality:
\[ m - 6 + 6 > 3 + 6 \]
\[ m > 9 \]
So, we have found the solution for the first inequality: \( m > 9 \).
Now, let's solve the second inequality \( m - 6 < -16 \):
\[ m - 6 < -16 \]
To isolate \( m \), we can add 6 to both sides of the inequality:
\[ m - 6 + 6 < -16 + 6 \]
\[ m < -10 \]
So, we have found the solution for the second inequality: \( m < -10 \).
Combining the solutions for both inequalities, we have:
\[ m > 9 \text{ or } m < -10 \]
Therefore, the solution is any value of \( m \) that is greater than 9 or less than -10.