Understanding Coefficients and Equations

This lesson introduces the concept of truth and equations, focusing on new notation for multiplication involving variables. It explains the role of coefficients in algebraic expressions and provides examples and non-examples. The lesson also covers how to determine solutions to equations and differentiate between true and false equations through practical examples.

What is the new way of representing multiplication in algebra?

• Using a subtraction sign

• Placing a number next to a variable

• Using a division sign

• Using a plus sign

In the expression 2x, what is the term '2' referred to as?

• Variable

• Exponent

• Coefficient

• Constant

Which of the following is NOT a coefficient?

• In 7z, the number 7

• In 1/2m, the number 1/2

• In x + 5, the number 5

• In 3y, the number 3

What is a solution to an equation?

• A value that makes the equation false

• A value that changes the equation

• A value that simplifies the equation

• A value that makes the equation true

If 2 + x = 12, what is the value of x?

• 10

• 14

• 12

• 2

Which of the following values for x, y, and z makes the equation xy = z true?

• x = 1, y = 10, z = 5

• x = 3, y = 4, z = 10

• x = 2, y = 6, z = 12

• x = 5, y = 5, z = 20

Which of the following is a false equation for xy = z?

• x = 1/2, y = 24, z = 12

• x = 4, y = 10, z = 40

• x = 2, y = 6, z = 12

• x = 100, y = 20, z = 5

If x = 4 and y = 10, which value of z would make xy = z false?

• 1000

• 40

• 400

• 100

What does the equation xy = z imply?

• x plus y equals z

• x divided by y equals z

• x times y equals z

• x minus y equals z

Which of the following is a true equation for xy = z?

• x = 1, y = 10, z = 20

• x = 2, y = 6, z = 10

• x = 5, y = 5, z = 25

• x = 3, y = 4, z = 12