Equations with Variables on Both Sides

In this video tutorial, Stan Forester introduces Lesson 7.1, focusing on solving equations with variables on both sides. The lesson uses algebra tiles as a visual aid to demonstrate the process of solving equations like x + 5 = 3x - 1. The tutorial explains how to rearrange terms, create zero pairs, and verify solutions using algebra tiles. Additionally, a real-world example involving rental car charges is presented to illustrate the application of these concepts. The video emphasizes the importance of strategic thinking in simplifying equations and avoiding errors.

What is the main focus of Lesson 7.1?

• Solving one-step equations

• Solving equations with variables on both sides

• Graphing linear equations

• Factoring polynomials

What do the yellow squares represent in algebra tiles?

• Negative units

• Unknowns

• Single units

• Zero pairs

How are negative numbers represented in algebra tiles?

• Green bars

• Yellow squares

• Red squares

• Blue circles

What is the first step in solving the equation x + 5 = 3x - 1 using algebra tiles?

• Adding the opposite of the x value

• Adding the opposite of the constant term

• Combining all variables on one side

• Dividing both sides by 2

After adding the opposite of the x value, what is the next step?

• Adding the opposite of the constant term

• Multiplying both sides by 2

• Combining all constants on one side

• Dividing both sides by 2

What is the value of x in the equation x + 5 = 3x - 1 after solving it?

• 2

• 5

• 3

• 4

How can you verify the solution to x + 5 = 3x - 1 using algebra tiles?

• By factoring the equation

• By substituting the value of x back into the equation

• By graphing the equation

• By using the quadratic formula

In the rental car example, what is the initial fee for Andy's rental car?

• $36

• $20

• $30

• $28

What is the daily charge for Buddy's rental car?

• $36

• $20

• $28

• $30

How many days will it take for the total charges of Andy's and Buddy's rental cars to be the same?

• 8 days

• 6 days

• 5 days

• 4 days