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Let's solve the inequality given in the problem: 

### \( 6(2 - x) \geq -4x + 8 \)

#### Step 1: Expand the left-hand side.
Distribute the \(6\) to both terms inside the parentheses:
\[
6(2 - x) = 12 - 6x
\]
Now the inequality becomes:
\[
12 - 6x \geq -4x + 8
\]

#### Step 2: Combine like terms.
Move all terms involving \(x\) to one side and the constants to the other side. First, add \(6x\) to both sides:
\[
12 \geq 2x + 8
\]
Now subtract \(8\) from both sides:
\[
4 \geq 2x
\]

#### Step 3: Solve for \(x\).
Divide both sides by 2:
\[
2 \geq x
\]
This can also be written as:
\[
x \leq 2
\]

Thus, the solution to the inequality is \(x \leq 2\).

#### Conclusion:
The correct answer is **B**, which corresponds to \(x \leq 2\).

---

Would you like further details or have any other questions? Here are five related questions to deepen your understanding:

1. How would the solution change if the inequality sign were flipped?
2. What happens if the coefficient of \(x\) on one side is negative?
3. How can you graph the inequality \(x \leq 2\)?
4. How would you check if a specific value, like \(x = 1\), satisfies the inequality?
5. Can you describe how inequalities are used in real-life scenarios?

**Tip:** When solving inequalities, remember that multiplying or dividing both sides by a negative number flips the inequality sign.

Which of the following inequalities describes all of the solutions to 6(2 − x) ≥ −4x + 8?

Learn how to solve the inequality 6(2 − x) ≥ −4x + 8 with a detailed step-by-step solution. This problem covers key algebraic concepts like the distributive property and solving inequalities. Suitable for students in Grades 8-10.

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