Let's solve the inequality step by step:

Given inequality: $-2x + 4 \geq -8$

Step 1: Isolate the term with $x$

First, subtract 4 from both sides of the inequality: $-2x + 4 - 4 \geq -8 - 4$ This simplifies to: $-2x \geq -12$

Step 2: Solve for $x$

Now, divide both sides by $-2$. Remember, when dividing or multiplying both sides of an inequality by a negative number, the inequality sign flips: $x \leq \frac{-12}{-2}$ $x \leq 6$

Final answer:

$x \leq 6$

Let me know if you'd like more details or have any questions!

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Here are five related questions to expand your understanding:

1. How does the solution change if we reverse the inequality $-2x + 4 \leq -8$?
2. What happens when multiplying or dividing an inequality by a negative number?
3. How would you express the solution on a number line?
4. Can you write the solution in interval notation?
5. How would you verify if a given value of $x$ satisfies the inequality?

Tip: Always flip the inequality sign when multiplying or dividing by a negative number!