Answer:
x ≤ -2 OR x ≥ 4
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Step-by-step explanation:
We are given the inequality:
|2x - 2| ≥ 6
Getting rid of the Modulus:
Since 2x-2 is in modulus:
|2x-2| = -(2x-2) OR 2x-2
(since the modulus of both these values is 2x-2)
Hence, our inequality can be written in 2 different ways:
- 2x-2 ≥ 6 (if 2x-2 ≥ 1)
- -(2x - 2) ≥ 6 (if 2x-2 < 0)
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Solving these 2 inequalities:
Solving inequality 1:
2x - 2 ≥ 6
2x ≥ 8 [adding 2 on both sides]
x ≥ 4 [dividing both the sides by 2]
This is the solution of the inequality if: 2x-2 ≥ 0
Solving Inequality 2:
-(2x-2) ≥ 6
It can be rewritten as:
2 - 2x ≥ 6
2 ≥ 6 + 2x [adding 2x on both the sides]
-4 ≥ 2x [Subtracting 6 from both sides]
x ≤ -2 [Dividing both sides by 2]
This is the solution of the given inequality if: 2x-2 < 0
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Solution of the given Inequality:
Therefore, the solution of the given inequality |2x-2| ≥ 6 are:
x ≥ 4 (if 2x-2 ≥ 0)
x ≤ -2 (if 2x-2 < 0)
Hence, option C is correct!
