QuestionExpress the inequality $x<-6$ or $x>7$ in interval notation.

Studdy Solution

STEP 1

Assumptions1. The inequality is given as $x<-6$ or $x>7$ . . We want to express this inequality in interval notation.

STEP 2

Interval notation is a way of writing subsets of the real number line. An interval is written as a pair of numbers, with the smaller number listed first. The numbers are separated by a comma and the pair is enclosed in parentheses or brackets, depending on whether the endpoints are included in the interval.In this case, the inequality $x<-6$ means that $x$ is less than -6. In interval notation, this is expressed as $(-∞, -6)$ . The parenthesis around -6 indicates that -6 is not included in the interval.

STEP 3

Similarly, the inequality $x>7$ means that $x$ is greater than7. In interval notation, this is expressed as $(7, ∞)$ . The parenthesis around7 indicates that7 is not included in the interval.

STEP 4

Because the original inequality is an "or" statement, we combine the two intervals using the union symbol, ∪, which represents the union of two sets. The union of two sets is a set containing all elements that are in either of the two sets.
So, the interval notation for the given inequality is $(-∞, -6) ∪ (7, ∞)$ .
The solution to the inequality $x<-6$ or $x>7$ is $(-∞, -6) ∪ (7, ∞)$ .

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