Question

Which compound inequality is represented by the graph?

Answer 1

For this case, the first thing you should do is observe the solution set.
 We have then that the set of solution is given by:
 (-inf, -4) U [3, inf)
 Therefore, we have:
 For (-inf, -4):
 x <-4
 For [3, inf):
 x ≥ 3
 Thus, the inequality in the graph is:
 x <-4 and x ≥ 3
 Answer:
 x <-4 and x ≥ 3

Answer 2

The correct option is $\boxed{\bf option 2}$.

Further explanation:

A compound inequality contains two or more inequalities such that they are separated by either “and” or “or”.

The Figure 1 (attached in the end) represents the compound inequality as $(-\infty,-4)$ and $[3,\infty)$.

Now $-4$ is excluded in the Figure 1 as the circle is hollow and $3$ is included in the Figure 1 as it is filled.

Option (1)

Here, the option (1) is $x$ or $x\geq 3$.

This represents that the value of $x$ lies in the interval $(-\infty,-4)$ as $-4$ is excluded in $x$ or the value of $x$ lies in the interval $[3,\infty)$ as $3$ is included in $x\geq 3$.

But either one of the possibility is true as the option contains “or”.

So, option (1) is incorrect.

Option (2)

Here, the option (2) is $x$ and $x\geq 3$.

This represents that the value of $x$ lies in the interval $(-\infty,-4)$ as $-4$ is excluded in $x$ and the value of $x$ lies in the interval $[3,\infty)$ as $3$ is included in $x\geq 3$.

Both the conditions of the given compound inequality is satisfied.

So, option (2) is correct.

Option (3)

Here, the option (3) is $x\leq -4$ or $x$.

This represents that the value of $x$ lies in the interval $(-\infty,-4]$ as $-4$ is included in $x\leq -4$ or the value of $x$ lies in the interval $(-\infty,3)$ as $3$ is excluded in $x$.

But neither one of the possibility is true as compared to the given compound inequality.

So, option (3) is incorrect.

Option (4)

Here, the option (4) is $x\geq -4$ and $x$.

This represents that the value of $x$ lies in the interval $(-\infty,-4]$ as $-4$ is included in $x\geq -4$ and the value of $x$ lies in the interval $(-\infty,3)$ as $3$ is excluded in $x$.

But neither one of the possibility is true as compared to the given compound inequality.

So, option (4) is incorrect.

Thus, the correct option is $\boxed{\bf option 2}$

Learn more

1. Learn more about the whole numbers are positive integers brainly.com/question/1852063.

2. Learn more about the adding and simplifying the numbers brainly.com/question/894273

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Number system

Keywords: Inequalities, compound inequality, interval, number line, real numbers, integers, whole numbers, open interval, closed intervals, semi closed intervals, semi-open intervals.