all real numbers that are greater than 4 or less than -4
To find all real numbers that are greater than 4 or less than -4, we need to consider two separate cases: numbers greater than 4 and numbers less than -4.
1. Numbers greater than 4: Any number greater than 4 falls into this category. To express this mathematically, we use the inequality symbol ">" which means "greater than." So, we can write this as x > 4, where "x" represents any real number greater than 4.
2. Numbers less than -4: Any number less than -4 falls into this category. To express this mathematically, we use the inequality symbol "<" which means "less than." So, we can write this as x < -4, where "x" represents any real number less than -4.
To combine both cases, we use the logical operator "or." Therefore, the set of all real numbers that are greater than 4 or less than -4 can be represented as the union of the two inequalities:
x > 4 OR x < -4
Alternatively, we can also write it as a compound inequality:
x < -4 OR x > 4
Both notations represent the same set of real numbers.