Exploring Two-Column Algebraic Proofs

What are the two main components of a two-column proof?

• Problems and Answers

• Equations and Solutions

• Statements and Justifications

• Questions and Explanations

Which property of equality is used when subtracting the same number from both sides of an equation?

• Division Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Addition Property of Equality

In Example 1, what is the first step to solve 9 - 4x = -19?

• Add 9 to both sides

• Subtract 9 from both sides

• Multiply both sides by 4

• Divide both sides by -4

What property of equality is used when multiplying both sides of an equation by the same number?

• Subtraction Property of Equality

• Division Property of Equality

• Multiplication Property of Equality

• Addition Property of Equality

In Example 2, what is the final step to prove x = -9?

• Divide both sides by -6

• Multiply both sides by 6

• Subtract 3 from both sides

• Add 3 to both sides

Which property of equality is used when distributing a number across terms inside parentheses?

• Division Property of Equality

• Addition Property of Equality

• Multiplication Property of Equality

• Distributive Property

In Example 3, what is the first step to solve -3(4x + 1) = 21?

• Add 3 to both sides

• Subtract 1 from both sides

• Divide both sides by -3

• Distribute -3 to each term inside the parentheses

What is the next step after distributing in Example 3?

• Add 3 to both sides

• Subtract 3 from both sides

• Multiply both sides by -3

• Divide both sides by -3

In Example 4, what is the first step to solve 28 - 6x = 2x - 84?

• Multiply both sides by 2

• Divide both sides by -6

• Subtract 2x from both sides

• Add 6x to both sides

What is the final step to prove x = 14 in Example 4?

• Divide both sides by -8

• Multiply both sides by -8

• Subtract 28 from both sides

• Add 28 to both sides