The correct answer is Option (4) → A, B, C only
Analyzing the Number Line
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The Region to the Left: There is a solid ray starting at $-5$ and going toward $-\infty$. This represents all values where $x \leq -5$.
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The Region to the Right: There is a solid ray starting at $5$ and going toward $\infty$. This represents all values where $x \geq 5$.
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The Dots: The dots at $-5$ and $5$ are solid (closed), meaning those specific numbers are included in the solution set.
Given Options:
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A ($x \geq 5$): This correctly describes the right-hand side of the graph.
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B ($x \leq -5$): This correctly describes the left-hand side of the graph.
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C ($|x| \geq 5$): This is the absolute value representation of the union of A and B. It means "the distance from zero is 5 or more," which covers both $x \geq 5$ and $x \leq -5$.
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D ($|x| > 5$): This is incorrect because it uses a "greater than" sign without the "equal to" component, which would require open circles on the graph.
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E ($|x| \leq 5$): This is incorrect because it represents the interval between $-5$ and $5$ (the unshaded part of this graph).
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