**What is Subtraction Property of Equality?**

According to the property, **if we subtract the same number in both side of the balanced equation, the equation will be still balanced and valid**.

Example

Let the given algebraic expression is:

4x + 2 = 3

If we subtract number 6 on both sides, the equation will be still balanced

4x + 2 – 6 = 3 – 6

Simplifying further

4x – 4 = -3

Generally, we can expressed the property as follows:

Where, A, B & x can be any possible number

**How Subtraction Equality Property works?**

Suppose you have been given a balanced algebraic equation

2x + 7 = 10

Imagine the expression as a balanced see-saw in which 2x + 7 is present on left and 10 is present on right.

Now subtract b on both sides.

Since you are doing subtraction on both sides, the equation will still be balanced

2x + 7 – b = 10 – b

**What will happen if b is subtracted only on one side?**

In this case the equation will get unbalanced.

**Conclusion** : In order to ensure equation is valid, make sure you do the subtraction on both sides.

**How this Subtraction Equality Property helpful?**

With the help of this property we can solve complex algebra problems in easy and fast steps.

**Example**

Consider the below equation and find value of x

4x + 8 = 24

Using Subtraction Equality Property;

Subtract number 8 on both the sides of equation so that number with x variable remain on left side

4x + 8 – 8 = 24 – 8

4x = 16

x = 16/4 = 4

Hence, taking the help of this property math equations can be solved with less hassle

**Subtraction Property of Equality Example**

**Example 01**

Solve the below equation and find value of x

x + 6 = 11

Subtract 6 on both sides so that only x variable remain on the left

x + 6 – 6 = 11 – 6

x = 5

hence, the value of x is 5

**Example 02**

Solve the below equation and find value of x

3x + 7 = 28

Subtracting both sides by 7 so that on left only x variable remain

3x + 7 – 7 = 28 – 7

3x = 21

x = 7

Hence, the value of x is 7

**Variables on one side**

Here we will solve equation by combining all variable x on one side and simple numbers on the other side

**Example 01**

Find the value of x

6x + 6 – 4x + 2 = 6

Combine number with x on one side and plain numbers on the other

6x – 4x + 6 + 2 = 6

2x + 8 = 6

Subtract 8 on both sides so that only x variable remain on left

2x + 8 – 8 = 6 – 8

2x = -2

x = -2/2 = – 1

Hence the value of x is -1

**Example 02**

Find the value of variable a

11 = a + 6 – 8 + 4a + 6a

Combine the variable a on one side and plain numbers on the other

11 = a + 4a + 6a + 6 – 8

11 = 11a – 2

Add +2 on both sides so that only variable A left on one side

11 + 2 = 11a – 2 + 2

13 = 11 a

13/11 = a

Hence, the value of a is 13/11

**Variable on both the side of equation**

Given are examples of equation in which variable is at both the side of equation.

**Example 01**5x = 4x + 3

First remove variable x from right side of equation by subtracting 4x on both sides

5x – 4x = 4x – 4x + 3

x = 3

Hence the value of x is 3

**Example 02**

13x + 7 = 10x

Remove the variable x from the right by subtracting 10x on both sides

13x – 10x + 7 = 10x -10x

3x + 7 = 0

Subtract -7 on both sides so that only variable x remain on left

3x + 7 – 7 = 0 – 7

3x = -7

x =-7/3

Hence x = – 7/3 is the value of x

**Multiple** **Variable on both sides**

**Example 01**6x + 3 = 4x + 7x +10

Add the variables present in one side

6x + 3 = 11x + 10

Remove variable from left by subtracting 6x on both sides

6x – 6x + 3 = 11x – 6x + 10

0 + 3 = 5x + 10

subtract 10 on both sides

3 – 10 = 5x + 10 – 10

-7 = 5x

x = -7/5

Hence, the value of x is (-7/5)

**Example 02**7 (x + 3) = 4x + 28

Use the distributive property to remove parenthesis

A (B + C) = A.B + A.C

7x + 21 = 4x + 28

Subtract 4x on both sides

7x – 4x + 21 = 4x – 4x + 28

3x + 21 = 28

Subtract 21 on both sides

3x + 21 – 21 = 28 -21

3x = 7

x = 7/3

Hence, value of x is 7/3

**Frequently asked question : Subtraction Property of Equality**

**(01) Is there any addition property of equality?**

Yes!!

If we add numbers on both sides of balanced equation, the equation will still remain balanced.

Suppose ax + b = c is a balanced equation

if we add d on both sides, the equation will still be balanced

ax + b + d = c + d

**(02) How this subtraction property of equality different from distributive property?**

In distributive property, we simplify the already given equation with multiplication and subtraction.

A . ( B + C ) = A.B + A.C

On the other hand subtraction property of equality says that subtracting numbers on both side of the equation will still make the equation valid and balanced

**(03) Will the equality property works for division also?**

Yes!!

In any balanced equation if you divide the expression on both sides, the equation will still be valid.

\mathtt{\frac{ax+b}{d} \ =\frac{c}{d}}