Solving Equations and Properties of Operations

This video covers Math 7 Unit 6 Lesson 3, focusing on reasoning with tape diagrams. It begins with finding equivalent expressions using the distributive and commutative properties. The lesson progresses to matching equations with tape diagrams and solving equations using these diagrams. The session concludes with homework instructions and a summary emphasizing the flexibility of tape diagrams in representing relationships between quantities.

Which property allows you to change the order of multiplication in an expression?

• Associative Property

• Identity Property

• Distributive Property

• Commutative Property

What is the result of applying the distributive property to 7 * (2 - 3n)?

• 14 - 21n

• 7 + 3n

• 14 + 21n

• 7 - 3n

Which equation matches a tape diagram with two X's and a 5 summing to 19?

• 2x = 19

• 2x + 5 = 19

• 5x + 2 = 19

• x + 5 = 19

How can you represent the equation 19 = 5 + 2x using a tape diagram?

• Five groups of x + 2

• A single group of 19

• Two groups of 5 + x

• Two groups of x + 5

What is the first step in solving 3x + 18 = 114 using a tape diagram?

• Subtract 18 from both sides

• Add 18 to both sides

• Multiply both sides by 3

• Divide both sides by 3

In the lesson summary, what is emphasized about tape diagrams?

• They can represent multiple equations

• They are not useful for complex equations

• They are only used for addition

• They can only represent one equation

What is the mental solution for the equation 2x = 10?

• x = 2

• x = 5

• x = 10

• x = 20

In a magic square, what must be true about the sums of rows, columns, and diagonals?

• They must all be prime numbers

• They must all be the same

• They must all equal zero

• They must all be different

How do you solve for x in the equation 35 = 8 + 6x?

• Divide both sides by 6

• Multiply both sides by 6

• Subtract 8 from both sides

• Add 8 to both sides

If a car travels 135 miles in 3 hours, what is its speed in miles per hour?

• 40 mph

• 45 mph

• 35 mph

• 30 mph