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Adding the same number to both sides of an equation results in an equivalent equation. Let a, b, and c be real numbers.
If a = b, then a + c = b + c.
Subtracting the same number from both sides of an equation results in an equivalent equation. Let a, b, and c be real numbers.
If a = b, then a - c = b - c.
LHS- 2=RHS- 2
Simplify left-hand side
Subtract terms
Given an equation, multiplying each side of the equation by the same number yields an equivalent equation. Let a, b, and c be real numbers.
If a = b, then a * c = b * c.
The Multiplication Property of Equality is an axiom, so it does not need a proof. This property is one of the Properties of Equality that can be used when solving equations. Consider the following example. x÷4&=2 x÷4 * 4&=2 * 4 x&=8
Here, by multiplying both sides of the equation by 4, the variable x was isolated and the solution of the equation was found. Note that the Multiplication Property of Equality also holds true if a, b, and c are complex numbers.Dividing each side of an equation by the same nonzero number yields an equivalent equation. Let a, b, and c be real numbers.
If a = b and c≠ 0, then a ÷ c = b ÷ c.
The Division Property of Equality is an axiom, so it does not need a proof to be accepted as true. This property is one of the Properties of Equality that can be used when solving equations. 5x&=10 5x ÷ 5&=10 ÷ 5 x&=2
As can be observed, by dividing both sides of the equation by 5, the variable x was isolated and the solution of the equation was found. Note that the Division Property of Equality also holds true if a, b, and c are complex numbers.For any real number, the number is equal to itself.
a=a
This property is an axiom, so it does not need a proof. This property is used to solve equations. For example, consider the equation below. x + 3 = 8
The sum on the left-hand side can be interpreted as a number, so this sum has to equal 8. This implies that x must be equal to 5.For all real numbers, the order of an equality does not matter. Let a and b be real numbers.
If a=b, then b=a.
For all real numbers, if two numbers are equal to the same number, then they are equal to each other. Let a, b, and c be real numbers.
If a=b and b=c, then a=c.
This property can be used together with other Properties of Equality to solve equations. x = 5y-30 5y-30 = 20 ⇒ x &=20
Since this property is an axiom, it does not need a proof to be accepted as true. The Transitive Property of Equality also holds true if a, b, and c are complex numbers.If two real numbers are equal, then one can be substituted for another in any expression.
If a=b, then a can be substituted for b in any expression.