Option (a) is correct as the compound inequality - 3 \(\leqslant\) x < 1 is represented by the graph.
Further explanation:
There are two types of the interval close interval and open interval.
If the values of x doesn’t includes the number than it is represented by hollow dot on the number line and if the values of x includes the number than it is represented by the solid dot on the number line.
Given:
The compound inequalities are listed below.
(a). - 3 \(\leqslant\) x < 1
(b). - 3 < x \(\leqslant\) 1
(c). x \(\leqslant\) - \(3{\text{ or }}x > 1\)
(d). x < - \(3{\text{ or }}x\) \(\geqslant\) 1
Explanation:
From the number line it has been shown that -3 is included in the value of x as it is shown by solid dot and 1 is not included as it is shown by hollow dot.
Option (a) is correct as the - 3 \(\leqslant\) x < 1 is represented by the graph.
Option (b) is not correct as the - 3 < x \(\leqslant\) 1 is not represented by the graph.
Option (c) is not correct as the x \(\leqslant\) - \(3{\text{ or }}x>1\) is not represented by the graph.
Option (d) is not correct as the \(x<-3{\text{ or }}x\geqslant1\) is not represented by the graph.
Hence, option (a) is correct as the compound inequality \(-3\leqslant x<1\) is represented by the graph.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Compound inequalities
Keywords: inequalities, graph, compound inequality, graph representation, number line, close interval, open interval.
