To solve the inequality $2(x-8) + 2x \geq -4$, follow these steps:

1. Distribute the 2 on the left side of the inequality: $2 \cdot (x - 8) + 2x \geq -4$ $2x - 16 + 2x \geq -4$

2. Combine like terms: $(2x + 2x) - 16 \geq -4$ $4x - 16 \geq -4$

3. Add 16 to both sides to isolate the term with the variable: $4x - 16 + 16 \geq -4 + 16$ $4x \geq 12$

4. Divide both sides by 4 to solve for $x$: $\frac{4x}{4} \geq \frac{12}{4}$ $x \geq 3$

The solution to the inequality is $x \geq 3$.

Would you like more details or have any questions? Here are some related questions:

1. How can we graph the solution $x \geq 3$ on a number line?
2. What are the steps to solve an inequality that includes a variable on both sides?
3. How do you check if your solution to an inequality is correct?
4. Can inequalities have more than one solution? How can they be represented?
5. What is the difference between strict inequalities and inclusive inequalities (e.g., $>$ vs. $\geq$)?

Tip: When solving inequalities, always perform the same operation on both sides to maintain the balance of the inequality.