Question

question
express the interval using two different representations.
(-3, -1)
answer attempt 1 out of 2
, , ) ( , ( , ) -∞ ∞ ∪ < > ≤ ≥ or
inequality notation:
number line:
-12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12
touch and drag to plot line.
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Explanation:

Step1: Understand Interval Notation

The interval \((-3, -1)\) is an open interval, meaning it does not include the endpoints \(-3\) and \(-1\). In inequality notation, this means \(x\) is greater than \(-3\) and less than \(-1\).

Step2: Write Inequality Notation

Using the greater than (\(>\)) and less than (\(<\)) symbols, we represent the interval as \(-3 < x < -1\).

Step3: Represent on Number Line

For the number line, we draw an open circle at \(-3\) and \(-1\) (since the interval is open) and shade the region between them. The number line has marks at \(-12, -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 12\). We place open circles at \(-3\) and \(-1\) and draw a line segment connecting them.

Answer:

Inequality Notation: \(-3 < x < -1\)
Number Line: Open circles at \(-3\) and \(-1\) with a line segment between them.