**Constant definition**

In math, **any fixed value** is known as **constant**.**Any possible number** is a constant.

The number can be an integer, natural number, decimal, fraction or whole number.**For example**

Number 2 is a constant as the value is fixed and its value will not change no matter what happens.

Similarly digits 5, 0, 27, 100, -91 are all constants.

**Separating constant and non- constant**

Consider the algebraic expression;

The expression contain two parts; 2x and 10.

Here;

2x ⟹ is non constant function

10 ⟹ is a constant function

In the first entity 2x;

⟹ 2 is a constant digit

⟹ x is non constant

Since 2x are joined together, they are non-constant as the value of x changes, the total value of digit will also change.

Observe the above table.

Note that the value of 2x is changing with change in x value.

Thus, the expression 2x is a non constant value.

Now consider the number 10.

No matter what will be the value of x, the number 10 is fixed and will not change its value.

Hence, number 10 is a constant.

**Examples of Constants **

Apart from numerical digits, there are other entities whose value is fixed and doesn’t change with time.

**(a) Speed of Light**The speed of light is 299,792,458 m/s.

This value is constant and does not change.

**(b) Pi value (𝜋)** = 3.14

**(c) Number of days in a week** = 7

**Some examples of Non constant values**

**(a) Temperature**

Every day the temperature changes.

Some day it is hot and someday its freezing cold.

Hence, temperature is a non constant value.

**(b) Speed of car**

Speed of moving car changes throughout the journey.

Hence, the speed is a non constant value.

**Solved Problems on Constants**

**(01) Identity the constants in below algebraic equation**.

7x + 3 = 8y – 2

**Solution**

Solving the algebraic equation

7x + 3 = 8y – 2

7x – 8y = – 2 – 3

7x – 8y = -5

Now there are three entities left in the expression;

7x ⟹ Its a non constant value

8y ⟹ Non constant

-5 ⟹ Constant

Hence, -5 is the only constant in the algebraic equation.

**(02) Identify the constant value in below expression**

9x – 7x + 5y + 10 = 15

**Solution**

Let’s simplify the algebraic equation first

(9x – 7x) + 5y = 15 – 10

2x + 5y = 5

There are three entities in the expression:

2x ⟹ Non constant

5y ⟹ Non constant

5 ⟹ Constant

Hence, digit 5 is the constant value in the expression.

**(03) Check if the value ⟹ 2𝜋 is constant or not**

**Solution**

2𝜋 is made of two components; 2 and 𝜋

Both 2 and 𝜋 have fixed value and are constants.

The multiplication of constant with constant is also constant.

Constant x Constant = Constant

Hence, 2 . 𝜋 is a constant value.

Let’s find exact value of 2𝜋

⟹ 2. 𝜋

⟹ 2 x 3.14

⟹ 6.28

**(04) Identify the constant value in below expression**

\mathtt{\frac{2x}{3} \ +\ \frac{7y}{6} \ +9\ =\ 0}

**Solution**

The equation consists of three entities;

2x / 3 ⟹ Non Constant value

7y / 6 ⟹ Non Constant Value

9 ⟹ Constant value

**(05)** Given are some parts and attributes of human body. Identity the features and figure out which of the component are constants for human body.

General parts and attributes of humans are:

Eyes, Ear, Nose, Height and Weight.

**Solution**

Eyes, Ear and nose are the constants for human body.

Every human has:

2 Eyes

2 Ears

1 Nose

On the other hand, height and weight are the non constant values.

Each person in the world have different height and weight, hence their value is not fixed for every human.

**Usefulness of Constants in Math**

Constants **helps to identify the variable value** in algebraic equation.

Consider the below equation.

Find the value of x which satisfies the equation.

5x + 7 = 17

**Solution**

The equation consists of following entities:

5x ⟹ Non Constant value

7 ⟹ Constant value

17 ⟹ Constant value

**Simplifying the equation;**

5x = 17 – 7

5x = 10

x = 10 / 5

x = 2

Hence x =2 satisfy the above equation.**Verification**

Put x = 2 in the equation

5x + 7 = 17

5 (2) + 7 = 17

10 + 7 = 17

17 = 17

L.H.S = R.H.S

The equation is satisfied.

**Conclusion**The constants help us to solve algebraic equations