Question

Which compound inequality is represented by the graph?



–2 < x ≤ 4
–2 ≤ x < 4
x < –2 or x ≥ 4
x ≤ –2 or x > 4

Answer 1

Answer-

$\boxed{\boxed{x < -2\ or\ x \geq 4}}$

Solution-

As we know that, on the number line, if a number is on the right of another number, then the former number is greater than the later number.

As, the number on the right side are 4, 5, ...so on (4 is dotted so it is included)

So the inequality will be $x\geq 4$

As, the number on the left side are -3, -4, -5, ..... so on (-2 is not dotted so it is excluded)

So the inequality will be $x<-2$

Then the compound inequality will be, $x < -2\ or\ x \geq 4$

Answer 2

Option (c) is correct as the compound inequality $\boxed{x <  - 2{\text{ or }}x \geqslant 4}$ 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). $- 2 < x \leqslant 4$

(b). $- 2 \leqslant x < 4$

(c). $x <  - 2{\text{ or }}x \geqslant 4$

(d). $x \leqslant  - 2{\text{ or }}x > 4$

Explanation:

From the number line it has been shown that -2 is not included in the value of x as it is shown by hollow dot and 4 is included as it is shown by solid dot.

Option (a) is not correct as the $- 2 < x \leqslant 4$ is not represented by the graph.

Option (b) is not correct as the $- 2 \leqslant x < 4$ is not represented by the graph.

Option (c) is correct as the $x <  - 2{\text{ or }}x \geqslant$ 4 is represented by the graph.

Option (d) is not correct as the $x \leqslant  - 2{\text{ or }}x > 4$ i s not represented by the graph.

Hence, Option (c) is correct as the compound inequality $\boxed{x <  - 2{\text{ or }}x \geqslant 4}$ 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.