Solving Linear Equations and Properties

Mrs. Apia's lesson covers solving linear equations using the distributive property and properties of equality. Students learn to simplify equations, handle negative signs, and recognize when equations have no solution. The lesson includes examples and a summary of key concepts.

What is the primary focus of the lesson introduced by Mrs. Apia?

• Exploring the history of mathematics

• Learning about geometric shapes

• Solving linear equations using the distributive property

• Understanding quadratic equations

In Example 1, what is the first step to solve the linear equation?

• Subtract terms from both sides

• Add all terms on both sides

• Multiply both sides by a constant

• Use the distributive property to expand terms

What property is used to simplify the expression 3 times the quantity 4x plus 7?

• Commutative Property

• Associative Property

• Identity Property

• Distributive Property

How do you verify if x equals 1 is a solution to the equation in Example 1?

• By graphing the equation

• By substituting x with 1 in the original equation

• By solving a different equation

• By using a calculator to find the derivative

In Example 2, what does the negative sign in front of a group of terms indicate?

• To add all terms

• To multiply all terms by zero

• To take the opposite of each term

• To ignore the terms

What is the result of simplifying 20 plus 9 minus 2 minus 3x?

• 27 plus 3x

• 27 minus 3x

• 29 plus 3x

• 29 minus 3x

In Example 4, what conclusion is drawn when 2 equals negative 3?

• The equation has a unique solution

• The equation has no solution

• The equation has infinite solutions

• The equation is incorrect

What is the first step in solving the equation in Example 4b?

• Multiply both sides by 2

• Divide both sides by 2

• Subtract 18x from both sides

• Add 18x to both sides

What is the purpose of using the distributive property in solving equations?

• To add terms

• To simplify and expand expressions

• To divide terms

• To subtract terms

Which property is used to rearrange terms in an equation?

• Distributive Property

• Commutative Property

• Identity Property

• Inverse Property