Question

express the interval using two different representations.
$x < -7$ or $x > -4$
answer attempt 1 out of 2
, , ) ( , ( , ) $-\infty$ $\infty$ $\cup$ $<$ $>$ $\leq$ $\geq$ or
interval 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: Analyze \( x < -7 \)

For \( x < -7 \), in interval notation, it's \( (-\infty, -7) \) because \( x \) can go to negative infinity (not including -7, so open parenthesis).

Step2: Analyze \( x > -4 \)

For \( x > -4 \), in interval notation, it's \( (-4, \infty) \) because \( x \) can go to positive infinity (not including -4, so open parenthesis).

Step3: Combine with union

Since it's "or", we use the union symbol \( \cup \) to combine the two intervals. So the interval notation is \( (-\infty, -7) \cup (-4, \infty) \).

Step4: Number line representation

• For \( x < -7 \): On the number line, we draw an open circle at -7 (since -7 is not included) and an arrow pointing to the left (towards negative infinity).
• For \( x > -4 \): On the number line, we draw an open circle at -4 (since -4 is not included) and an arrow pointing to the right (towards positive infinity).

Answer:

Interval Notation: \( (-\infty, -7) \cup (-4, \infty) \)
Number Line: Open circle at -7 with left arrow, open circle at -4 with right arrow.