# Subtraction Property of Equality : definition, examples & questions

## 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}}

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