What is the equivalent inequality for -3(x - 4) ≥ 9?

To solve the inequality -3(x - 4) ≥ 9, you first want to distribute the -3 to the terms inside the parentheses. This gives you -3x + 12 ≥ 9.

Next, you will isolate the variable -3x by subtracting 12 from both sides of the inequality. This results in -3x ≥ 9 - 12, which simplifies to -3x ≥ -3.

Now, to solve for x, divide both sides of the inequality by -3. It's important to remember that when you divide or multiply an inequality by a negative number, the direction of the inequality sign must be flipped. Thus, we have x ≤ -1.

The solution x ≤ -1 shows that any value of x that is less than or equal to -1 will satisfy the original inequality. Therefore, the correct equivalent inequality is indeed x ≤ -1, which corresponds to the correct option.