Exploring Always Equal Machines

The video tutorial covers the concept of equivalent expressions using a series of machine-based examples. The teacher explains how different expressions can yield the same output, demonstrating this through factored and expanded forms. Students are guided through challenges to identify and create equivalent expressions, using the distributive property and understanding the relationship between different forms. The lesson concludes with a series of exercises to reinforce the learning objectives.

What is the main takeaway from the introduction about the two machines with different expressions?

• The machines never produce the same output.

• The machines sometimes produce the same output.

• The machines always produce different outputs.

• The machines always produce the same output.

When will the new machines with expressions x-2 and 2-x have equal outputs?

• Never

• Always

• Sometimes

• Only when x is negative

What are expressions called that give the same output for every input?

• Opposite expressions

• Similar expressions

• Different expressions

• Equivalent expressions

Which of the following values, when plugged into the expressions 3(4x-5) and 12x-15, shows they are equivalent?

• x = 1

• x = 0

• x = 2

• x = -1

What is the expanded form of 2 times (10 - x)?

• 10 - 2x

• 10 + 2x

• 20 + 2x

• 20 - 2x

Which expression is equivalent to 2 times (10 - x)?

• 20 + 2x

• 2x - 20

• 20 - 2x

• 10 - 2x

What is the expanded form of -5 times (8 - 2x)?

• -40 - 10x

• -40 + 10x

• 40 - 10x

• 40 + 10x

Which of the following is an equivalent expression to -15 + 6x?

• -3(5 - 2x)

• 3(2x - 5)

• 3(5 - 2x)

• -3(5 + 2x)

Why can we switch the order of terms when adding but not when subtracting?

• Because neither operation is commutative.

• Because addition is commutative and subtraction is not.

• Because subtraction is commutative and addition is not.

• Because both operations are commutative.

Which of the following is NOT an equivalent expression to -15 + 6x?

• 15 + 6x

• -3(5 - 2x)

• 3(2x - 5)

• 6x - 15