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# Not Equal|Definition & Meaning

## Definition

A synonym for **unequal** is the sign that says **not equal**. The **symbol** for “inequality” is represented by the **not equal sign**. The purpose of this is to **demonstrate** a juxtaposition of the two **quantities,** which are **not equal** and therefore **represent** inequality among themselves.

When a **number** does not have an **equivalent** in another number, we refer to that **relationship** as not equal. It is **denoted** by the symbol $\neq$, which consists of two **horizontal** lines that are parallel to one another and are cut by such an **inclined vertical line. **

## Explanation of Not Equal

**Not equal** is simple to **understand** because it represents a **comparison** of two **numbers** or **quantities** that are not equal. In everyday situations, we use them **everywhere.**

The not **equal** term has a lot of **applications** in **real-life scenarios.** For example, **John** visited a **fruit** vendor in order to purchase **4** **pounds** of oranges. The **fruit** seller put them on his scale to see how much they **weighed** and he found that the weight of the orange was 8 pounds which is not equal to **4** **pounds. Therefore** **4** **pounds** are not equal to **8** **pounds**

**Another situation** where the use of **not equal** can be seen is if **Alia** needs to calculate the **areas** of **squares** with **sides** that are 2 **inches** and 5 **inches** long. **She** calculates the **area** of **each square** using the **square formula,** arriving at the **conclusion** that a **square** has a surface area of 4 **square** inches for sides that are 2 **inches** long and **25 square inches** for sides that are 5 inches long. As a result, it can be that the two given **squares** do **not** have the **same size.**

**Thus,** you can now easily find the **comparison** between the **two quantities** or **numbers** which are not equal. The following figure represents the visual representation of not equal.

## Visual Representation of Not Equal

We use the **circle-based** diagram below to **illustrate** the idea of not equal:

**Suppose** we have a **circle** and we **split** it into two **unequal** parts. The two **unequal** portions of **A and B** with values of **10** and **90,** respectively, are **depicted** in the circle in **Figure** 2.

The **circle** in the above **illustration** is the result of **splitting** the **circle** into three **unequal pieces.** Three unequal portions of **A, B, and C,** with values of **10,70,** and **20,** respectively, are **depicted** in the circle in **Figure** 3.

If we split the **same** circle with **different** values or **unequal** values of A, B, C, and D. We get a **circle** which is **represented** in **figure** 3. The **values** of A and B in this **scenario** are **10** and **20** respectively while the values of C and D are **30** and **40 respectively.**

## Numerical Example of Not Equal

The **teacher** of **Adnan** asked him to solve the two equations which are 4a+60 = 80, 5a +90=120, 5a + 90 = 140, 5a + 90 = 150, and 5a + 90 = 160. **Determine whether** or not an is **equal** to 2.

### Solution

**First,** we have to find the value of **a** for the **first equation.** We are **given** that:

**4a + 60 = 80**

So, we have to find the value of a. **Subtracting 60** from both sides **results** in:

**4a + 60 – 60 = 80 – 60**

**4a = 80 – 60**

**4a = 20**

**Dividing** 4 on both **sides results** in the following:

**4a/4 = 20/4**

**a = 20/4**

**a=5**

**Therefore,** it is concluded that the value of a is **not equal** to the given value of a. Thus 2 is not **equal** to 5.

Now, **we** have to find the value of a for the **2nd** equation. We are **given** that:

**5a + 90 = 120**

So, we have to find the **value** of a. **Subtracting** 90 from both sides **results** in:

**5a + 90 – 90 = 120 – 90**

**5a = 120 – 90**

**5a = 30**

**Dividing** 5 on both sides **results** in the following:

**5a/5 = 30/5**

**a = 30/5**

**a=6**

**Therefore,** it is **concluded** that the value of a is **not equal** to the **given** value of a. Thus 2 is not **equal** to 6.

Now, we have to find the value of a for the **3rd equation.** We are given **that:**

**5a + 90 = 140**

So, we **have** to find the value of a. **Subtracting** 90 from both **sides** results in:

**5a + 90 – 90 = 140 – 90**

**5a = 140 – 90**

**5a = 50**

Dividing 5 on both sides results in the following:

**5a/5 = 50/5**

**a = 50/5**

**a=10**

**Therefore,** it is concluded that the **value** of a is not equal to the given value of a. Thus 2 is **not equal** to 10.

Now, we **have** to find the value of a for the **4th equation.** We are given that:

**5a + 90 = 150**

So, we have to find the **value** of a. **Subtracting 90** from both sides results in:

**5a + 90 – 90 = 150 – 90**

**5a = 150 – 90**

**5a = 60**

**Dividing** 5 on both **sides results** in the following:

**5a/5 = 60/5**

**a = 60/5**

**a=12**

**Therefore,** it is concluded that the value of a is **not equal** to the given value of a. Thus **2** is not equal to **12.**

Now, we have to **find** the value of a for the **5th equation.** We are given that:

**5a + 90 = 160**

So, we have to **find** the value of a. **Subtracting** 90 from **both** sides **results** in:

**5a + 90 – 90 = 160 – 90**

**5a = 160 – 90**

**5a = 70**

**Dividing** 5 on **both** sides **results** in the following:

**5a/5 = 70/5**

**a = 70/5**

**a=14**

**Therefore,** it is **concluded** that the value of a is **not** equal to the **given** value of a. We can **easily** say that the two **numbers** are not equal. **Thus** 2 is **not equal** to **14.**

*All mathematical drawings and images were created with GeoGebra.*