Characteristics of Solutions in Equations

Mrs. Lopez combines lessons six and seven of module four for grade eight, focusing on solving linear equations. The lesson covers translating word problems into number problems, solving equations with variables on both sides, and determining if equations have one, multiple, or no solutions. Examples demonstrate the use of the distributive property, identifying no solution, and infinite solutions. The lesson concludes with exercises for students to practice the concepts learned.

What is the main focus of the combined lessons 6 and 7?

• Solving equations with variables on both sides

• Studying probability

• Learning about geometry

• Understanding fractions

In example 1, what property is used to simplify the equation?

• Associative Property

• Commutative Property

• Distributive Property

• Identity Property

What is the solution for x in example 1?

• x = 0

• x = 2

• x = 3

• x = 1

In example 3, what conclusion is drawn when 33 equals 34?

• The equation is unsolvable

• The equation has infinite solutions

• The equation has no solution

• The equation has a unique solution

What indicates that an equation has no solution?

• Same coefficients and same constants

• Different coefficients and same constants

• Different coefficients and different constants

• Same coefficients and different constants

In example 5, what is observed about the equation 7x - 3 = -3 + 7x?

• It has a unique solution

• It has no solution

• It has infinite solutions

• It is unsolvable

What is a characteristic of equations with infinite solutions?

• Different coefficients and same constants

• Same coefficients and different constants

• Different coefficients and different constants

• Same coefficients and same constants

In the exercises, what is the solution for x in the equation 3x + 5 = 4x + 7?

• x = -1

• x = 2

• x = 1

• x = -2

What type of solution does the equation 3x + 5 = 3x - 3 have?

• No solution

• Unsolvable

• Unique solution

• Infinite solutions

What is the solution for x in the equation 3x + 5 = 4x + 7?

• x = -1

• x = 1

• x = 2

• x = -2