Question

Illustrate the set \left\\{ x:-3\le x<0\,\,or\,x>2;x\in R \right\\} on a real number line.

Answer 1

To illustrate the given condition on the number line we need to carefully observe the condition given and express the range of the variable $x$ on the number line. The condition is \left\\{ x:-3\le x<0\,\,or\,x>2;x\in R \right\\}. That means the value $x$ lies between $0$ and $-3$. The value of $x$ is also greater than $2$.

Complete step-by-step solution:
To represent the given inequality on the line, evaluate the inequality.
Given one condition is $x$ is greater than $-3$. That means the range lies to the right side of the number $-3$ .
Next the number $0$ is greater than $x$. That means the range of $x$ lies to the left side of $0$
Another condition is $x>2$ .
That means the value of $x$ lies to the right of $2$ .and it is greater than $2$.
The set \left\\{ x:-3\le x<0\,\,or\,x>2;x\in R \right\\} when expressed on a real number line is as given below

The set is given by the points marked on the number line.

Additional information: Equalities which are the equations where LHS is equal to RHS, the graphs developed will be a single curve or line. For an inequality, the range may differ with respect to the numerical given. We can define the inequality as a not equal comparison of any two numerical or mathematical expressions.

Note: In the given inequality there are two conditions which do not intersect. The inequalities can be solved separately. And hence the set given in question is not a continuous function. It is an irregular one. The set can be considered as a subset of real numbers as the elements of the set lie within the range of real numbers.