To solve the inequality \( 2(-3m - 5) \geq -28 \), we will start by distributing the 2 on the left side:
\[ 2(-3m) + 2(-5) \geq -28 \]
This simplifies to:
\[ -6m - 10 \geq -28 \]
Next, we'll isolate the term involving \( m \) by adding 10 to both sides:
\[ -6m - 10 + 10 \geq -28 + 10 \]
This simplifies to:
\[ -6m \geq -18 \]
Now, divide both sides by -6. Remember that when dividing or multiplying both sides of an inequality by a negative number, the inequality sign reverses:
\[ m \leq 3 \]
Thus, the solution to the inequality is:
\[ m \leq 3 \]