Solving Equations Using Properties

This lesson teaches how to solve equations using mathematical properties. It covers the distributive, associative, and multiplicative inverse properties, providing examples and justifications for each step. Common mistakes are identified and corrected, and students are guided through solving equations with visual aids and step-by-step instructions. The lesson concludes with a summary of the key concepts and methods learned.

What does the distributive property allow you to do in an equation?

• Distribute a multiplication over addition

• Multiply a number by its reciprocal

• Add the same number to both sides

• Move parentheses to simplify

Which property states that multiplying a number by its reciprocal results in one?

• Distributive Property

• Associative Property

• Additive Inverse Property

• Multiplicative Inverse Property

What is the first step in solving the equation 2x + 6 = 10?

• Divide both sides by 2

• Multiply both sides by 2

• Add 6 to both sides

• Subtract 6 from both sides

After using the distributive property, what is the next step in solving 2x - 6 = 4?

• Divide both sides by 2

• Multiply both sides by 2

• Subtract 6 from both sides

• Add 6 to both sides

What is the result of dividing both sides of the equation 2x = 10 by 2?

• x = 10

• x = 5

• x = 20

• x = 2

Which property allows you to rearrange parentheses in an equation?

• Additive Inverse Property

• Distributive Property

• Associative Property

• Multiplicative Inverse Property

What is the final value of x in the equation 9 + 3x = 5x - 7 after solving?

• x = 10

• x = 9

• x = 8

• x = 7