The picture shown below illustrates the difference between a variable and a constant.

The symbol which has no fixed value is called as variable. Example : x, y, z |
The symbol which has a fixed value is called as constant Example : 2, 3, 2/3, 0.57, -2, -3 |

Cost of a garment |
Value of $100 currency |

**Constant : **

Let us consider $100 currency.

What is the value of $100 currency when i have it in Newyork ?

Its value is $100.

What is the value of $100 currency when i have it in Sancfrancisco ?

Its value is $100.

What is the value of $100 currency when i have it in Chicago?

Its value is $100

From the above questions and answers, one thing is very clear. That is,. in whichever part of America i go, the value of the currency $100 is same. It is not changed in different parts of the country.

So $100 is constant.

**Variable : **

Let us consider a garment whose cost is x dollars.

The manufacturer of the garment sells it to the wholesaler at the cost of $40.

So, x = $40.

The wholesaler sells it to the retailer at the cost of $44.

So x = $44.

The retailer sells it to the customer at the cost of $50.

So x = $50

Here, the garment is same.

But, when it is in manufacturer, wholesaler and retailer, its cost is different.

Hence, the cost of the garment x is variable.

Some English alphabets will have fixed values, but the values will be unknown.

For example, let k be arbitrary constant.

Then, k will have only one fixed value and it is unknown.

Let us look at some problems on simple equations to have better understanding on variables.

**Problem 1 : **

Solve for x :

x - 2 = 0

**Solution : **

x - 2 = 0

Add 2 to each side.

x = 2

So, the value of x is 2.

**Problem 2 : **

Solve for x :

9x = 27

**Solution : **

9x = 27

Divide each side by 9.

x = 3

So, the value of x is 3.

**Problem 3 : **

Solve for x :

x + 3 = -2

**Solution : **

x + 3 = -2

Subtract 3 from each side.

x = -5

So, the value of x is -5.

**Problem 4 : **

Solve for x :

3x + 6 = 18

**Solution :**

3x + 6 = 18

Subtract 6 from each side.

3x = 12

Divide each side by 3.

x = 4

So, the value of x is 4

In all the above problems, we have got value for the same alphabet x.

Even though we have the same alphabet x, we don't get the same value for x.

We get different value for x. So the value of x is being changed.

Therefore, x is considered to be variable.

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