Math

QuestionFind the simplest interval form of the set (,1][6,)(-\infty,-1] \cap[-6, \infty).

Studdy Solution

STEP 1

Assumptions1. The given set is (,1][6,)(-\infty,-1] \cap[-6, \infty). We need to express the set in the simplest interval form3. The symbol \cap represents the intersection of two sets, which includes all elements that are common to both sets4. The symbol (,1](-\infty,-1] represents all real numbers less than or equal to -15. The symbol [6,)[-6, \infty) represents all real numbers greater than or equal to -6

STEP 2

To express the set in the simplest interval form, we need to find the intersection of the two given intervals. This means we need to find all the real numbers that are common to both intervals.

STEP 3

The first interval, (,1](-\infty,-1], includes all real numbers less than or equal to -1.

STEP 4

The second interval, [6,)[-6, \infty), includes all real numbers greater than or equal to -6.

STEP 5

The intersection of these two intervals will be all the real numbers that are both less than or equal to -1 and greater than or equal to -.

STEP 6

This means the intersection of the two intervals is [6,1][-6, -1].So, the set (,1][6,)(-\infty,-1] \cap[-6, \infty) can be expressed in the simplest interval form as [6,1][-6, -1].

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