# Interval Notation with Compound Inequalities

## Interval Notation With Compound Inequalities - How it Works - Video

### Example 1

Example 1:

Interval notation is another way to write domain or the input values.

In this example we have a compound inequality, from 1 to 8 but not including 1 and 8. To denote that we do not include 1 and 8, we use less than.

When we use interval notation, we use parenthesis to denote that we are not including the number and brackets to include the number. So the interval notation in this example is (1, 8).

### Example 2

Example 2:

Interval notation is another way to write domain or the input values.

In this example we have a compound inequality, from 22 to 28 but not including 22. To denote that we do not include 22, we use less than and to denote that we include 29, we use less than or equal to.

When we use interval notation, we use parenthesis to denote that we are not including the number and brackets to include the number. So the interval notation in this example is (22, 29].

### Example 3

Example 3:

Interval notation is another way to write domain or the input values.

In this example we have a compound inequality, from -18 to -11 but not including -11. To denote that we do not include -11, we use less than and to denote that we include -18 we use less than or equal to.

When we use interval notation, we use parenthesis to denote that we are not including the number and brackets to include the number. So the interval notation in this example is [-18, -11).

### Example 4

Example 4

Interval notation is another way to write domain or the input values.

In this example we have a compound inequality, from 14 to 21. To denote that we include 14 and 21 we use less than or equal to.

When we use interval notation, we use parenthesis to denote that we are not including the number and brackets to include the number. So the interval notation in this example is [14, 21].

### Example 5

Example 5:

Interval notation is another way to write domain or the input values.

In this example we have a compound inequality, x < 3 or 6 < x. Another way to say this is from -∞ to 3, not including 3 or 6 to +∞, but not including 6. To denote that we do not include 3 or 6, we use less than.

When we use interval notation, we use parenthesis to denote that we are not including the number and brackets to include the number. So the interval notation in this example is (-∞, 3) U (6, +∞), where the U or union is for an or statement.

### Example 6

Example 6:

Interval notation is another way to write domain or the input values.

In this example we have a compound inequality, x ≤ -6 or -3 < x. Another way to say this is from -∞ to -6 or -3 to +∞, but not including -3. To denote that we include -6 we use less than or equal and to denote that we do not include -3, we use less than.

When we use interval notation, we use parenthesis to denote that we are not including the number and brackets to include the number. So the interval notation in this example is (-∞, -6] U (-3, +∞), where the U or union is for an or statement.

### Example 7

Example 7:

Interval notation is another way to write domain or the input values.

In this example we have a compound inequality, x < 11 or -3 ≤ x. Another way to say this is from -∞ to 11, but not including 11 or 14 to +∞. To denote that we include 14 we use less than or equal and to denote that we do not include 11, we use less than.

When we use interval notation, we use parenthesis to denote that we are not including the number and brackets to include the number. So the interval notation in this example is (-∞, 11) U [14, +∞), where the U or union is for an or statement.

### Example 8

Example 8:

Interval notation is another way to write domain or the input values.

In this example we have a compound inequality, x ≤ -9 or -6 ≤ x. Another way to say this is from -∞ to -9 or -6 to +∞, but not including -3. To denote that we include -9 and -6 we use less than or equal.

When we use interval notation, we use parenthesis to denote that we are not including the number and brackets to include the number. So the interval notation in this example is (-∞, -9] U [-6, +∞), where the U or union is for an or statement.