Option (a) is correct as the compound inequality - 3 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 x < 1
(b). - 3 < x 1
(c). x -
(d). x < - 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 x < 1 is represented by the graph.
Option (b) is not correct as the - 3 < x 1 is not represented by the graph.
Option (c) is not correct as the x - is not represented by the graph.
Option (d) is not correct as the is not represented by the graph.
Hence, option (a) is correct as the compound inequality 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.