Question

Which compound inequality is represented by the graph?

Answer 1

Answer:

$-3 \leq x$

Step-by-step explanation:

we have

The solution of the inequality represented by the graph is equal to the interval

$[-3,1)$

All real numbers greater than or equal to $-3$ and less than $1$

so

$x\geq-3$

$x$

therefore

$-3 \leq x$

Answer 2

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 $x$ is not represented by the graph.

Hence, option (a) is correct as the compound inequality $-3\leqslant x$ is represented by the graph.

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Compound inequalities

Keywords: inequalities, graph, compound inequality, graph representation, number line, close interval, open interval.