HOW TO CONVERT INTERVAL NOTATION TO INEQUALITY

An open interval does not include its endpoints, and is enclosed in parentheses.

A closed interval includes its endpoints, and is enclosed in square brackets.

An interval is considered bounded if both endpoints are real numbers. An interval is unbounded if both endpoints are not real numbers.

Convert interval notation to inequality notation or vice versa. Find the endpoints and state whether the interval is bounded, its type, and graph the interval.

Example 1 :

[-6, 3)

Solution :

From the interval, we find more than one value. Let us consider every value as x.

Converting the given interval into inequality, we get

-6 ≤ x < 3

So, the possible values of x are {-6, -5, -4, -3, ......2}.

By drawing the possible solutions in number line, we get

Example 2 :

(-∞, -1)

Solution :

From the interval, we find more than one value. Let us consider every value as x.

Converting the given interval into inequality, we get

-∞ < x < -1

By drawing the possible solutions in number line, we get

Example 3 :

[-2, 3]

Solution :

From the interval, we find more than one value. Let us consider every value as x.

Converting the given interval into inequality, we get

-2 ≤ x  ≤ 3

By drawing the possible solutions in number line, we get

Example 4 :

Use an inequality to describe the interval of real numbers.

(i)  [-1, 1)   (ii)  (-∞, 4]

Solution :

(i) Possible solutions are -1, 0. By writing it using inequality, we get

-1 ≤ x < 1

(ii)  Possible solutions are

...........-1, 0, 1,........4.

By writing it using inequality, we get

-∞ < x ≤ 4

Example 5 :

Use an inequality to describe the interval of real numbers.

Solution :

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