Understanding the Distributive Property of Equality in Mathematics | A Tool for Solving Equations

Distributive Property of Equality

The Distributive Property of Equality is a property in mathematics that allows us to multiply or divide both sides of an equation by the same value without changing the truth of the equation

The Distributive Property of Equality is a property in mathematics that allows us to multiply or divide both sides of an equation by the same value without changing the truth of the equation. It is derived from the Distributive Property of Multiplication.

The Distributive Property of Multiplication states that for any three numbers a, b, and c, the product of a and the sum of b and c is equal to the sum of the products of a and b, and a and c. In mathematical notation, it can be represented as:

a * (b + c) = (a * b) + (a * c)

The Distributive Property of Equality applies this principle to equations. It tells us that if two expressions are equal to each other, and we multiply or divide both sides of the equation by the same value, the resulting equation will still be true.

For example, let’s say we have the equation 2x + 4 = 12. To solve for x, we can use the Distributive Property of Equality to isolate the variable:

2x + 4 = 12
2x + 4 – 4 = 12 – 4 (Subtract 4 from both sides)
2x = 8

Now, to solve for x, we divide both sides of the equation by 2 (the coefficient of x):

2x/2 = 8/2
x = 4

By using the Distributive Property of Equality, we successfully solved for x. Keep in mind that this property can be applied to both addition/subtraction and multiplication/division equations.

In summary, the Distributive Property of Equality allows us to multiply or divide both sides of an equation by the same value, preserving the truth of the equation. This property plays a crucial role in solving equations and manipulating expressions in algebra.

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