To solve the inequality \(-2w \leq 12\), divide both sides by \(-2\). Remember that when dividing by a negative number, the inequality sign flips:

\[
w \geq -6
\]

So the solution is \(w \geq -6\). 

Do you want details on how to solve inequalities or have any questions? Here are some related questions you might consider:

1. What does it mean for \(w\) to be greater than or equal to \(-6\)?
2. How would you graph this inequality on a number line?
3. Can you give examples of values for \(w\) that satisfy this inequality?
4. What happens if the inequality is changed to a strict inequality (i.e., \(<\) instead of \(\leq\))?
5. How would you solve a similar inequality with a different constant? 

**Tip:** When solving inequalities, always pay attention to the direction of the inequality sign, especially when multiplying or dividing by negative numbers.

Discover how to solve the inequality -2w <= 12 step-by-step. This lesson covers key algebraic concepts, including the properties of inequalities and how to handle negative coefficients. Ideal for students in Grades 7-9.

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