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.
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
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
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
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
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
The value of x is 86/15
Variable on both side of equation
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
10x + 2 = 16x
Subtract 10x on both sides to remove variable x from left
10x – 10x + 2 = 16x – 10x
2 = 6x
The value of x is 2/6
Multiple variable on both sides
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)
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?
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?
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