Properties & Algebraic Proofs Quiz

Which property justifies the step from 4x = 28 to x = 7?

• Addition Property of Equality

• Division Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

What is the first step in a two-column proof?

• Write the given statement

• State the conclusion

• Solve the equation

• List the reasons

Which property is used when replacing a variable with a number?

• Symmetric Property

• Transitive Property

• Reflexive Property

• Substitution Property

What does the Distributive Property state?

• a(bc) = (ab)c

• a + b = b + a

• a - b = b - a

• a(b + c) = ab + ac

Which property is used to justify that a value always equals itself?

• Substitution Property

• Symmetric Property

• Reflexive Property

• Transitive Property

In the equation -9(2x - 3) = 63, what is the first step to solve for x?

• Distribute -9

• Add 3 to both sides

• Subtract 27 from both sides

• Divide by -9

Which property is used to justify the step from -18x + 27 = 63 to -18x = 36?

• Addition Property of Equality

• Division Property of Equality

• Multiplication Property of Equality

• Subtraction Property of Equality

What is the final step in solving the equation 5y - 1 = 14?

• Add 1 to both sides

• Multiply both sides by 5

• Divide both sides by 5

• Subtract 1 from both sides

Which property is used to justify the step from -15x = -10 to x = 2/3?

• Subtraction Property of Equality

• Division Property of Equality

• Multiplication Property of Equality

• Addition Property of Equality

What is the reason for the step from 2(x - 9) = -10 to 2x - 18 = -10?

• Distributive Property

• Subtraction Property of Equality

• Addition Property of Equality

• Division Property of Equality