Solving Equations and Proportionality

This video covers questions 6 to 9 from a state testing practice test. It begins with simplifying expressions to find equivalent expressions for the perimeter of a garden. The video then explains how to determine the constant of proportionality in equations. It also analyzes real-world scenarios to identify when the answer is zero, using the additive inverse property. Finally, it demonstrates creating and solving a two-step equation to find the cost of renting movies.

What is the first step in simplifying the expression for the perimeter of the larger garden?

• Distribute the constants

• Ignore the parentheses

• Combine like terms

• Multiply the terms

After combining like terms, what is the simplified expression for the perimeter of the larger garden?

• 2x + 20

• 4x + 40

• 2x + 40

• 4x + 20

Which property is used to simplify the expression 2 * (2x + 20)?

• Identity Property

• Associative Property

• Distributive Property

• Commutative Property

What is the constant of proportionality in the equation y = 4x?

• 1

• 3

• 12

• 4

Which equation has a constant of proportionality equal to 4?

• 4y = x

• y = 3x

• y = 4x

• 3y = 4x

In which situation would the answer to the question be zero?

• Teddy swam 8 feet up after sinking 8 feet

• Jerry walked 1.5 miles west and then 1.5 miles east

• The temperature changes from -3°C to 3°C

• A trail changes elevation from -50 ft to 50 ft

What is the change in elevation if a trail starts at -50 ft and ends at 50 ft?

• 0 ft

• 50 ft

• 100 ft

• 150 ft

What is the difference in temperature between -3°C and 3°C?

• 6°C

• 3°C

• 0°C

• 9°C

What is the first step in solving the equation 4.75 + 3x = 11.50?

• Subtract 4.75 from both sides

• Divide both sides by 3

• Multiply both sides by 3

• Add 4.75 to both sides

What is the cost of renting each movie if Jessica rented one video game for $4.75 and three movies for a total of $11.50?

• $3.00

• $4.00

• $2.25

• $1.75