Answer:
x < -5 or x > 5
(∞, -5) ∪ (5, ∞)
Explanation:
The bars either side of an expression or a value are the absolute value symbol. The absolute value of a real number 'x' is the distance of 'x' from zero on the number line. It is denoted by |x| and is always a non-negative value.
The inequality |x| > 5 represents the absolute value of x being greater than 5.
To solve this inequality, we can consider two cases: when x is positive (x > 0) and when x is negative (x < 0).
Case 1: x > 0
In this case, the inequality simplifies to x > 5.
Case 2: x < 0
In this case, the inequality simplifies to -x > 5.
This can be rewritten as x < -5 by multiplying both sides by -1 (remembering to change the direction of the inequality sign since we are multiplying by a negative number).
Solution
Combining both cases, the solution to the inequality |x| > 5 is:
This means that x can be any number less than -5 or any number greater than 5.
The solution in interval notation is (∞, -5) ∪ (5, ∞).