CONVERT INEQUALITIES TO INTERVAL NOTATION

1. If we have the inequality

< (less than) or > (greater than),

we have to use the empty / unfilled circle.

2. If we have the inequality sign 

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

we have to use the filled circle.

Example 1 :

x ≤ 7

Solution :

Let us represent the given inequality in the number line.

x ≤ 7

Here, we have the sign ≤ (less than or equal). So, we have to use filled circle.

Hence the required interval notation is (-∞, 7]

Example 2 :

x ≥ -1/2

Solution :

x ≥ -1/2

Here, we have the sign ≥ (greater than or equal). So we have to use filled circle.

Hence the required interval notation is [-1/2, ∞)

Example 3  :

-8 < x ≤ 10

Solution  :

-8 < x ≤ 10

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

Hence the required interval notation is (-8, 10]

Example 4  :

-14 < x < -2

Solution  :

-14 < x < -2

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

Hence the required interval notation is (-14, -2)

Example 5  :

-3/4 < x < 1/2

Solution  :

-3/4 < x < 1/2

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

Hence the required interval notation is (-3/4, 1/2)

Example 6  :

x > 8

Solution  :

x > 8

Here, we have the sign > (greater than). So we have to use unfilled circle.

Hence the required interval notation is (8, ∞)

Example 7  :

x ≤ -2 or x ≥ 0

Solution  :

x ≤ -2 or x ≥ 0

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] u [0, ∞)

Example 8  :

x < 0 or x > 2

Solution  :

x < 0 or x > 2

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

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

Hence the required interval notation is (-∞, 0) u (2, ∞)

Example 9  :

x < 27

Solution  :

x < 27

Here, we have the sign < (less than). So we have to use unfilled circle.

Hence the required interval notation is (-∞, 27)

Example 10  :

x > 5

Solution  :

x > 5

Here, we have the sign > (greater than). So we have to use unfilled circle.

Hence the required interval notation is (5, ∞)

Example 11  :

-6 < x < 6

Solution  :

-6 < x < 6

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

Hence the required interval notation is (-6, 6)

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