We are given a graph of compound inequality.
Given options are :
–3 ≤ x < 1
–3 < x ≤ 1
x ≤ –3 or x > 1
x < –3 or x ≥ 1.
In the graph, we can see that we have a solid dot on -3 and a hollow dot on 1.
Please note: A solid dot represents ≤ or ≥ inequality sign, because the number also included on which we have a solid dot.
And a hollow dot represents only < or > inequality sign.
Option (a) is correct as the compound inequality [tex]\boxed{ - 3 \leqslant x < 1}[/tex] represented by the graph.
Further explanation:
There are two types of the interval close interval and open interval.
If the values of [tex]x[/tex] doesn’t includes the number than it is represented by hollow dot on the number line and if the values of [tex]x[/tex] includes the number than it is represented by the solid dot on the number line.
Given:
The compound inequalities are listed below.
(a). [tex]- 3 \leqslant x < 1[/tex]
(b). [tex]- 3 < x \leqslant 1[/tex]
(c). [tex]x \leqslant - 3{\text{ or }}x > 1[/tex]
(d). [tex]x < - 3{\text{ or }}x \geqslant 1[/tex]
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 [tex]\boxed{ - 3 \leqslant x < 1}[/tex] 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.
