Question

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

second option

Explanation:

inequalities of the form | x | ≥ a , have solutions of the type

x ≤ - a OR x ≥ a

given

| 2x - 6 | ≥ 4 , then

2x - 6 ≤ - 4 ( add 6 to both sides )

2x ≤ 2 ( divide both sides by 2 )

x ≤ 1

OR

2x - 6 ≥ 4 ( add 6 to both sides )

2x ≥ 10 ( divide both sides by 2 )

x ≥ 5

then solution is

x ≤ 1 OR x ≥ 5