Math / Numbers & Operations

QuestionWrite the interval in set-builder notation. $(6,9]$ $\{x \mid 6<x \leq 9\}$ $\{x \mid x>9\}$ $\{x \mid-9 \leq x<-6\}$ $\{x \mid-\infty<x<\infty\}$ $\{x \mid x \leq 6\}$

Studdy Solution

STEP 1

1. The interval notation $(6, 9]$ describes a set of real numbers.
2. The notation $(a, b]$ means all real numbers $x$ such that $a < x \leq b$ .
3. Set-builder notation expresses sets by specifying a property that its members must satisfy.

STEP 2

1. Understand the interval $(6, 9]$ .
2. Translate the interval notation to set-builder notation.

STEP 3

Understand the interval $(6, 9]$ . This interval includes all real numbers $x$ such that $6 < x \leq 9$ .

STEP 4

Translate the interval $(6, 9]$ into set-builder notation. We express the interval as: $\{ x \mid 6 < x \leq 9 \}$
Solution: The interval $(6, 9]$ in set-builder notation is: $\{ x \mid 6 < x \leq 9 \}$

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