Question

10 points

Determine the solution to the inequality.

|2x − 6| ≥ 4

x ≤ 0 or x ≥ 6
x ≤ 1 or x ≥ 5
x ≤ −5 or x ≥ 5
x ≥ −5 or x ≤ 4

Answer 1

To solve this inequality, we need to split it into two cases based on the sign of 2x - 6.

If 2x - 6 is nonnegative, then the inequality becomes 2x - 6 >= 4, which simplifies to x >= 5.

If 2x - 6 is negative, then the inequality becomes -(2x - 6) >= 4, which simplifies to x <= 1.

Therefore, the solution to the inequality is x <= 1 or x >= 5, which is the same as the second answer choice x ≤ 1 or x ≥ 5.

The other answer choices are not valid solutions because they do not include all values of x that satisfy the inequality.