Answer:
(−∞,2)∪(8,∞)
Step-by-step explanation:
To solve the inequality |x - 5| > 3, we need to consider the definition of absolute value. The inequality |x - 5| > 3 means that the distance between x and 5 is greater than 3. This can be broken down into two separate inequalities:
1. x - 5 > 3
2. x - 5 < -3
Let's solve each of these inequalities separately:
1. x - 5 > 3
x > 8
2. x−5<−3
x<2
So, the solution to the inequality \(|x - 5| > 3\) is:
x<2 or x>8
In interval notation, this is written as:
(−∞,2)∪(8,∞)
So, the solution is all \(x\) such that \(x\) is less than 2 or greater than 8.
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