Answer:
x < -2 or x > 4
Explanation:
This is an absolute value inequality of the form
|X| ≥ b
where X is an expression with a variable, and b is a non-negative number.
An absolute value inequality of this form is solved by changing the form into a compound inequality using the word "or."
To solve
|X| ≥ a,
solve the compound inequality
X < - a or X > a
In other words, when the absolute value of an expression is greater than (or greater than or equal to) a number, rewrite the absolute value inequality as
expression < -number or expression > number
In your problem, you have
|2x - 2| ≥ 6
The expression is 2x - 2.
The number is 6.
You change the absolute value inequality to the following compound inequality:
2x - 2 ≤ -6 or 2x - 2 > 6
Now you solve each inequality always keeping the word "or" in between them.
2x - 2 ≤ -6 or 2x - 2 > 6
2x < - 4 or 2x > 8
x < -2 or x > 4
I hope you understand the solution and explanation. If you have any questions, ask in the comments.