<h3>
Answer:</h3>
x ≤ -2 OR x ≥ 4
__________________________________________________________
<h3>
Step-by-step explanation:</h3>
<u>We are given the inequality:</u>
|2x - 2| ≥ 6
Getting rid of the Modulus:
Since 2x-2 is in modulus:
|2x-2| = -(2x-2) OR 2x-2
<em>(since the modulus of both these values is 2x-2)</em>
Hence, our inequality can be written in 2 different ways:
- 2x-2 ≥ 6 <em>(if 2x-2 ≥ 1)</em>
- -(2x - 2) ≥ 6 <em>(if 2x-2 < 0)</em>
__________________________________________________________
<u>Solving these 2 inequalities:</u>
Solving inequality 1:
2x - 2 ≥ 6
2x ≥ 8 [<em>adding 2 on both sides]</em>
x ≥ 4 [<em>dividing both the sides by 2]</em>
This is the solution of the inequality if: 2x-2 ≥ 0
Solving Inequality 2:
-(2x-2) ≥ 6
<em>It can be rewritten as:</em>
2 - 2x ≥ 6
2 ≥ 6 + 2x [<em>adding 2x on both the sides]</em>
-4 ≥ 2x [<em>Subtracting 6 from both sides]</em>
x ≤ -2 [<em>Dividing both sides by 2]</em>
This is the solution of the given inequality if: 2x-2 < 0
__________________________________________________________
<u>Solution of the given Inequality:</u>
Therefore, the solution of the given inequality |2x-2| ≥ 6 are:
x ≥ 4 <em>(if 2x-2 </em>≥ 0)
x ≤ -2 <em>(if 2x-2 < 0)</em>
Hence, option C is correct!
