Question

How do you express interval [-2, 9] in terms of inequalities?

Answer 1

Hint: Now to write the interval in terms of inequalities we will consider the left term as the least bound of the inequality and the term on right as the greater bound of the inequalities. Since the square brackets are used we will use less than equal to and greater than equal to sign.

Complete step-by-step solution:
Now first let us understand what an interval means.
An interval represents a set of numbers which lies between the first digit and second digit.
Let us take an example to understand this.
Consider the interval (0,1).
This interval contains all the numbers which lie between 0 and 1.
Hence we can say that in general an interval (a,b) contains all the numbers that lie between a to b.
Now if we use parentheses to close or open the interval then the number is not included.
Which means if the interval is represented as (1,2) then it contains all the numbers between 1 and 2 excluding 1 and 2.
Now similarly if the interval is represented by square brackets then the numbers are to be included in the interval set. Hence the interval [1,2] represents all the numbers between 1 and 2 including 1 and 2.
Now consider the given interval [-2,9]
The interval contains all the numbers between -2 and 9 including -2 and 9.
Hence any number that lies in the interval is greater than or equal to -2 and less than or equal to 9.
Hence the interval [-2,9] can be written as $-2\le x\le 9$. Hence [-2,9] is expressed as $-2\le x\le 9$

Note: Now note that whenever square brackets are used we use the less than or greater than equal to sign and for parenthesis we use strictly less than sign. Hence the interval which is represented as $[a,b)$ is written as $a\le x< b$.