We can write

2 < x < 5

as x ∈ (2, 5)

This is called
**
interval notation
**

There are different types of intervals

- Open Interval (a < x < b)
- Closed interval (a ≤ x ≤ b )
- Semi Open Interval (a ≤ x < b and a < x ≤ b)

##
**
Write x > 2 in interval notation
**

So, x goes 2 to infinity

∴
**
x ∈ (2, ∞)
**

Note-∞ and -∞ always has an open bracket

##
**
Write x ≥ 3 in interval notation
**

**
**

**
**

So, x goes 3 to infinity

∴
**
x ∈ [3, ∞)
**

##
**
Write x < 5 in interval notation
**

So, x goes –infinity to 5

∴
**
x ∈ (–∞, 5)
**

Note-∞ and -∞ always has an open bracket

##
**
Write x ≤ –1 in interval notation
**

**
**

**
**

So, x goes –infinity to –1

∴
**
x ∈ (–∞, –1]
**

##
**
Write x ≤ -1 & x > 2 in interval notation
**

In this, we have two notations

**
x ≤ –1
**

and
**
x > 2
**

We merge both graphs

So, x goes –infinity to –1 and from 2 to infinity

So, in interval notation, we write it as

∴
**
x ∈ (–∞, –1] ∪ (2, ∞)
**

##
**
Write x < 5 & x > 2 in interval notation
**

In this, we have two notations

**
x
**
**
<
**
**
5
**

**
x
**
**
> 2
**

We merge both graphs

So, x goes 2 to 5

So, in interval notation, we write it as

∴
**
x ∈ (2, 5)
**