Solve for x. |4x - 1| >= 6; x \le or x \ge (Type integers or simplified fractions.)

Answer 1

There are two cases to consider:

Case 1: 4x - 1 is greater than or equal to 0 (|4x - 1| = 4x - 1)
In this case, the inequality becomes: 4x - 1 >= 6
Adding 1 to both sides, we have: 4x >= 7
Dividing both sides by 4, we get: x >= 7/4

Case 2: 4x - 1 is less than 0 (|4x - 1| = -(4x - 1) = -4x + 1)
In this case, the inequality becomes: -4x + 1 >= 6
Subtracting 1 from both sides, we have: -4x >= 5
Dividing both sides by -4 (and reversing the inequality), we get: x <= -5/4

Combining the two cases, the solution to the inequality is:
x <= -5/4 or x >= 7/4