Find the solution of
|x-2|>8
The answer is {1,4}
how?
consider when x<2
then -(x-2)>8
-x>8-2
x<-6
consider when x>2
then x-2>8
x>10
Now, you must have an answer that is wrong.
To find the solution to the equation |x-2| > 8, we can break it down into two separate inequalities and solve each one individually.
First, let's consider the case when (x-2) is positive:
(x-2) > 8
To solve this inequality, we add 2 to both sides:
x > 10
Now, let's consider the case when (x-2) is negative:
-(x-2) > 8
To solve this inequality, we multiply both sides by -1, which reverses the inequality:
x - 2 < -8
Next, we add 2 to both sides:
x < -6
So, we have two separate inequalities:
x > 10 and x < -6
To find the solution that satisfies both inequalities, we look for the overlapping region on a number line. The solution lies between -6 and 10, including -6 but not including 10. In interval notation, this can be represented as (-6, 10).
However, in the question, it states that the answer is {1,4}. That means there might have been some misunderstanding or error in the problem statement or answer provided. Please double-check the given problem and answer to ensure accuracy.