Final answer:
The inequality 4x - 3 ≥ 2(2x - 1) simplifies to a contradiction, which means there are no x-values that would make the inequality true. Therefore, none of the options provided are correct.
Step-by-step explanation:
To solve the inequality 4x - 3 ≥ 2(2x - 1), we first distribute the 2 on the right side of the inequality:
4x - 3 ≥ 4x - 2
Subtract 4x from both sides:
-3 ≥ -2
Which is not a true statement. This means that no matter what value x takes, the inequality will not hold true since -3 will never be greater than or equal to -2.
However, this does not mean there is no solution to the original inequality. Let's go back and carefully check our steps to see if we made an error.
Actually, by subtracting 4x from both sides, we get 0 ≥ 1, which is a contradiction. Since our steps up to this point were correct, this means the inequality has been simplified correctly, and there are no x-values that will satisfy it.
Therefore, all the given options a) x ≤ 1 b) x ≥ 1 c) x ≤ -1 d) x ≥ -1 are incorrect because the original inequality is not true for any x.