Option (a) is correct as the compound inequality \(\boxed{ - 3 \leqslant x < 1}\) 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 is 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.
The value of x lies between -3 to 1.
Option (a) is correct.
Option (b) is not correct.
Option (c) is not correct
Option (d) is not correct.
Hence, Option (a) is correct as the compound inequality \(\boxed{ - 3 \leqslant x < 1}\) 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.
