To solve the inequality \(-2(w - 4) \geq 12\), we can start by distributing the \(-2\) on the left side:
\[ -2w + 8 \geq 12 \]
Next, we subtract 8 from both sides:
\[ -2w \geq 12 - 8 \]
This simplifies to:
\[ -2w \geq 4 \]
Now, we divide both sides by \(-2\). Remember that when dividing by a negative number, we need to reverse the inequality sign:
\[ w \leq \frac{4}{-2} \]
This simplifies to:
\[ w \leq -2 \]
Thus, the equivalent inequality is:
\[ w \leq -2 \]