Expressions, Equations, and Proportionality

This video tutorial covers seventh grade unit 6, lesson 18 of illustrative mathematics. It includes four main problems: writing equivalent expressions using only addition, using the distributive property to simplify expressions, correcting a mistake in a number puzzle, and analyzing proportionality in energy output from power plants. The video concludes with a prompt to subscribe to the channel.

How can the expression '20 minus 9' be rewritten using only addition?

• 20 plus negative 9

• 20 plus 9

• 20 minus 9

• 20 minus negative 9

What is the equivalent expression for '4X minus 7Y' using addition?

• 4X minus 7Y

• 4X plus 7Y

• 4X plus negative 7Y

• 4X minus negative 7Y

Which of the following is the result of applying the distributive property to '9 times 4X minus 3Y'?

• 36X minus negative 27Y

• 36X plus negative 27Y

• 36X plus 27Y

• 36X minus 27Y

What is the result of 'negative 2 times negative 6X' using the distributive property?

• Positive 12X

• Negative 12X

• Positive 6X

• Negative 6X

How can 'one-fifth times 20Y' be simplified?

• 4Y

• 5Y

• 20Y

• One-fifth Y

What is the correct expression for the number puzzle: pick a number, add negative 2, and multiply by 5?

• X plus 10

• X minus 10

• 5 times X plus 2

• 5 times X minus 2

What is the constant of proportionality for the coal power plant's energy output?

• 1000

• 500

• 200

• 100

Is the energy output from the solar power plant proportional to the number of days?

• It is sometimes proportional

• Yes, it is proportional

• It is always proportional

• No, it is not proportional

What equation represents the relationship between days and energy for the coal power plant?

• Energy = Days / 500

• Energy = Days * 500

• Energy = Days + 500

• Energy = Days - 500

Why can't an equation be written for the solar power plant's energy output?

• There is no predictable relationship

• The energy output is too high

• The energy output is constant

• The number of days is too variable