Properties of Equality and Proofs

This video tutorial covers algebraic reasoning, focusing on properties of equality and their application in solving equations. It introduces two-column proofs, providing examples and guided practice to reinforce learning. The tutorial aims to equip students with the skills to identify and use algebraic properties effectively.

Which property of equality allows you to add the same number to both sides of an equation without changing the equality?

• Division Property

• Subtraction Property

• Addition Property

• Multiplication Property

What does the reflexive property state about any real number?

• It is equal to itself.

• It is equal to zero.

• It is equal to one.

• It is equal to its opposite.

In a two-column proof, what is typically found on the right side?

• The reasons for each step

• The given information

• The steps of the proof

• The final answer

What is the first step in solving the equation 4x - 1 = 27 using a two-column proof?

• Add 1 to both sides

• Multiply both sides by 4

• Subtract 1 from both sides

• Divide both sides by 4

Which property is used to justify dividing both sides of an equation by the same non-zero number?

• Division Property

• Multiplication Property

• Subtraction Property

• Addition Property

When simplifying an equation, what is the process of combining terms with the same variable called?

• Distributive Property

• Transitive Property

• Combining Like Terms

• Substitution

In the equation -7x + 4x, what is the result of combining like terms?

• 11x

• -3x

• 3x

• -11x

What property allows you to replace a variable with another variable that it is equal to?

• Substitution Property

• Symmetric Property

• Reflexive Property

• Transitive Property

In the equation a + b = 2c, if b = c, what property allows you to replace b with c?

• Substitution Property

• Multiplication Property

• Addition Property

• Division Property

What is the final step in solving the equation -36 = 4x using a two-column proof?

• Add 36 to both sides

• Subtract 36 from both sides

• Multiply both sides by 4

• Divide both sides by 4