CONVERT INEQUALITIES TO INTERVAL NOTATION

How to plot inequality on the number line ?

• If we have the inequality

< (less than) or > (greater than),

we have to use the empty / unfilled circle.

• If we have the inequality sign 

≤ (less than or equal to) or ≥ (greater than or equal to),

we have to use the filled circle.

To convert inequalities into interval notation, we need to know the table below.

Write these number sets using interval notation :

Example 1 :

{x│-1 ≤ x ≤ 6}

Solution :

-1 ≤ x ≤ 6

Here, we are having the both side signs ≤ (less than or equal to). So we have to use filled circle.

Hence, the required interval notation is [1, 6].

Example 2 :

{x│ 0 < x < 5}

Solution:

0 < x < 5

Here, we are having the both side signs < (less than). So have to use unfilled circle.

Hence, the required interval notation is (0, 5).

Example 3 :

{x│-4 < x ≤ 7}

Solution :

-4 < x ≤ 7

Here, we are having the both side signs < and ≤ (less than and less than or equal to). So have to use filled circle and unfilled circle.

Hence, the required interval notation is (-4, 7].

Example 4 :

{x│ 4 ≤ x < 8}

Solution :

4 ≤ x < 8

Here, we are having the both side signs < and ≤ (less than and less than or equal to). So have to use filled circle and unfilled circle.

Hence, the required interval notation is [4, 8).

Example 5 :

{x│ x ≤ 2 or x ≥ 5}

Solution :

Here, both inequalities are having the sign ≤ or ≥. So we have to use filled circle.

Since we have OR, we combine all the solution of both inequalities.

Hence, the required interval notation is (-∞,2] υ [5, ∞)

Example 6 :

 {x│ x < -3 or x > 4}

Solution :

Here, both inequalities are having the sign < or >. So we have to use unfilled circle.

Hence, the required interval notation is (-∞, 3) υ (4, ∞).

Example 7 :

 {x│ -1 < x ≤ 1 or x ≥ 2}

Solution :

Hence, the required interval notation is (-1, 1] υ [2, ∞)

Example 8 :

 {x│ x < -4 or 2 ≤ x < 7}

Solution :

Hence, the required interval notation is (-∞, 4) υ [2, 7).