Solving Linear Equations and Properties

Mrs. Lopez introduces linear equations, explaining their properties and how to solve them. She provides examples, demonstrating substitution and the use of the distributive property. Students are encouraged to practice with exercises and think critically about solutions.

What is a linear equation?

• An equation with only constants

• An equation with variables having exponents greater than 1

• An equation where one linear expression equals another

• An equation with no variables

In the equation 4 + 15x = 49, what is the solution when x = 3?

• x = 5

• x = 2

• x = 3

• x = 4

How do you verify if a number is a solution to a linear equation?

• By dividing the number by the equation

• By multiplying the number by the equation

• By substituting the number into the equation

• By adding the number to both sides

In the equation 8x - 19 = -4 - 7x, is x = 5 a solution?

• Yes, because both sides equal -21

• No, because both sides equal -39

• Yes, because both sides equal 21

• No, because both sides do not equal

What is the first step in solving an equation with variables on both sides?

• Divide both sides by the variable

• Add all constants to one side

• Multiply both sides by zero

• Combine like terms

What property is used to simplify the equation 3(x + 9) = 4x - 7 + 7x?

• Associative Property

• Distributive Property

• Commutative Property

• Identity Property

In the equation 3(x + 9) = 4x - 7 + 7x, is x = 5/4 a solution?

• No, because both sides do not equal

• Yes, because both sides equal 6

• Yes, because both sides equal 30

• No, because both sides equal 6

What mistake did Angel make in solving the equation 6x + 4 - x = 2(x + 1)?

• Multiplied instead of divided

• Added instead of subtracted

• Forgot to distribute

• Combined unlike terms

In the exercise, what is the solution to the equation 6x + 5 = 5x + 8 + 2x when x = -3?

• x = 3

• x = 0

• x = -3

• x = 1

What should you do if an equation has no solution?

• Multiply both sides by zero

• Check for errors in simplification

• Ignore the equation

• Add more variables