Properties of Equality

Front

What is the Distributive Property?

Back

The Distributive Property states that a(b + c) = ab + ac, meaning you can distribute a factor across a sum.

Front

What does the Substitution Property state?

Back

The Substitution Property states that if two values are equal, one can be substituted for the other in any expression.

Front

What is the Multiplication Property of Equality?

Back

The Multiplication Property of Equality states that if you multiply both sides of an equation by the same non-zero number, the two sides remain equal.

Front

How do you apply the Distributive Property in an equation?

Back

To apply the Distributive Property, multiply the term outside the parentheses by each term inside the parentheses.

Front

What is an example of using the Substitution Property?

Back

If x = 5, then in the expression 2x + 3, you can substitute 5 for x to get 2(5) + 3.

Front

What is the purpose of the Multiplication Property of Equality in solving equations?

Back

It allows you to eliminate fractions or simplify equations by multiplying both sides by the same number.

Front

Can you give an example of the Distributive Property in action?

Back

Yes, for example, 3(2 + 4) = 3*2 + 3*4, which simplifies to 6 + 12 = 18.

Front

What is the first step in solving the equation 3(x - 7) = 42?

Back

The first step is to apply the Distributive Property: 3x - 21 = 42.

Front

What is the last property you would use to solve the equation 4x - 5 = 17?

Back

The last property used would be the Addition Property of Equality to isolate x.

Front

How do you recognize when to use the Substitution Property?

Back

You use the Substitution Property when you have an equation with a known value that can replace a variable.