**What is Addition Property of Equality?**

The property says that** if we add numbers on both side of the balanced equation, the equation will still be balanced and valid**.

**Example**

Let the given equation is **Ax + By = C**

If we add** number D** on both sides, the equation will still be balanced

Ax + By + D = C + D

Generally the addition property of equality is expressed as:

Where A, B & x are real numbers

**Verification of addition property of equality**

Consider the below equation:**5 = 5** – – -(i)

Above equation is true & balanced.

**Add number 6 on both sides of equation**

5 + 6 = 5 + 6

**11 = 11 ** – – -(ii)

Even after adding numbers, the equation (ii) is still true.

**Hence, doing math operation on both side of equation does not affect equation quality.**

**How addition property of equality works**

Suppose you have been provided with following balanced equation

2x + 3 = 20

Imagine the equation as the below see-saw whose right and left weight are completely balanced

Now if you add any number on both side the equation will still be balanced.

Suppose you add number 10 on both sides. In this case, the see-saw is still balanced.

2x + 3 + 10 = 20 + 10

But if you add number only on one side, the balance get disturbed & the equation may not hold valid

**How is the property useful?**

In your higher mathematics class you will come across complex algebraic and calculus equation which will take lot of your time and energy.

On using this property you will be able to solve equation in fast and easy steps.

**Addition Property of equality examples**

**Example 01**

Solve the equation and find value of x

x – 8 = 12

Add 8 on both sides so that only variable x remains on left side

x – 8 + 8 = 12 + 8

x = 20

**Hence, the value of x is 20**

**Example 02**Solve the equation

5x – 15 = 65

Add 15 on both sides so that only variable x remain on left side

5x – 15 + 15 = 65 + 15

5x = 80

x = 16

**Hence, the value of x is 16**

**Multiple Variables on one side**

**Example 01**

11x – 14 – 3x + 4 = 7

11x – 3x – 14 + 4 = 7

8x – 10 = 7

Add 10 on both sides, so that only variable x remain on left

8x – 10 + 10 = 7 + 10

8x = 17

x = 17/8

**The value of x is 17/8**

**Example 02**

11 = 25 + 9x – 100 + 6x

11 = 25 – 100 + 9x + 6x

11 = -75 + 15x

Add 75 on both sides so that only variable x remains on right

11 + 75 = -75 + 75 + 15x

86 = 15x

x= 86/15

**The value of x is 86/15**

**Variable on both side of equation**

**Example 01**

6x = -3x + 16

Add 3x on both sides to remove variable x from right side

6x + 3x = -3x + 3x + 16

9x = 16

x = 16/9

**The value of x is 16/9**

**Example 02**

10x + 2 = 16x

Subtract 10x on both sides to remove variable x from left

10x – 10x + 2 = 16x – 10x

2 = 6x

x =2/6

**The value of x is 2/6**

**Multiple variable on both sides**

**Example 01**

16x + 9 – 21x = 3x + 5

16x – 21x + 9 = 3x + 5

-5x + 9 = 3x + 5

Add 5x on both sides

-5x + 5x + 9 = 3x + 5x + 5

9 = 8x + 5

Subtract 5 on both sides

9 – 5 = 8x + 5 -5

4 = 8x

x = 4/8 = 1/2

**Hence, the value of x is (1/2)**

**Example 02**12x + 33 + 13x = 17x – 63 – 45x

12x + 13x + 33 = 17x – 45x – 63

25x + 33 = -28x -63

Add 28x on both sides

25x + 28x + 33 = – 28x + 28x – 63

53x + 33 = – 63

Subtract 33 on both sides

53x + 33 – 33 = – 63 – 33

53x = -99

x = -99/53

**Hence, the value of x is -99/53**

**Frequently asked questions : Addition Property of Equality**

**(01) Will the property of equality work for subtraction also?**

Yes!!

There is a subtraction property of equality which says that if you subtract same number on both side of balanced equation, the equation will remain still valid.

if Ax + B = C is the given equation

Subtract number D on both sides of equation

Ax + B – D = C – D

This equation is valid and balanced

**(02) How Commutative property and Addition Property of equality different?**

Commutative property says that in addition, the change in the order of number will have no effect on the final result.

A + B = B + A

Addition property of equality is all about adding same number on both side of the equation.

A = B

A + C = B + C

**(03) Will the equality property works for multiplication?**

Yes!!

In a balanced equation, if you multiply a number on both side of the equation, it will still remain valid and balanced.

Let the given equation be: Ax + B = C

Multiply number D on both sides, we get:

D (Ax + B) = C. D

ADx + BD = CD

**(04) What are some other properties of addition?**

Some common addition properties are:

(a) Commutative Property of addition

(b) Associative Property

(c) Identity Property

(d) Distributive Property

(e) Inverse Property