Final answer:
The solution to the inequality 2(4 + 2x) ≥ 5x + 5 is x ≤ 3. Option A is correct.
Step-by-step explanation:
To solve the inequality 2(4 + 2x) ≥ 5x + 5, let's first distribute the 2 on the left side of the inequality:
8 + 4x ≥ 5x + 5
We then move all terms containing x to one side:
4x - 5x ≥ 5 - 8
Simplify the terms:
-x ≥ -3
Now, to get the inequality in terms of positive x, we will multiply both sides by -1, remembering to reverse the inequality sign, as multiplying or dividing by a negative number inverts the inequality:
x ≤ 3
The solution is that x must be less than or equal to 3, denoted as x ≤ 3.