Understanding Equations and Real-World Applications

This lesson covers writing two-step equations using algebra tiles and translating real-world scenarios into equations. It begins with an introduction to two-step equations, followed by modeling equations with algebra tiles. The lesson then explores changing equation signs and concludes with writing equations for real-world problems and creating scenarios for given equations.

What is the purpose of using algebra tiles in solving equations?

• To make the equation more complex

• To visualize the equation components

• To replace numbers with symbols

• To eliminate the need for calculations

In the equation 3x - 4 = 5, what do the tiles on the left side represent?

• Five negative constants

• Five positive variables

• Three negative variables and four positive constants

• Three positive variables and four negative constants

What does the line in the 'mat' represent in the context of algebra tiles?

• The multiplication operation

• The equal sign

• The addition operation

• The subtraction operation

How do you modify the equation 3x - 4 = 5 to -3x + 4 = 5 using algebra tiles?

• Use five negative constant tiles

• Use five positive variable tiles

• Use three positive variable tiles and four negative constant tiles

• Use three negative variable tiles and four positive constant tiles

What is the equation for a gym membership costing $460 with a $40 initiation fee and monthly payments?

• 460 + 12m = 40

• 40 + 12m = 460

• 460 + 40m = 12

• 12 + 40m = 460

If Billy has a $150 gift card and buys video games costing $35 each, what equation represents his remaining balance of $45?

• 35x - 150 = 45

• 150 + 35x = 45

• 45 - 35x = 150

• 150 - 35x = 45

What does the equation 5x + 50 = 120 represent in a real-world scenario?

• A movie ticket purchase

• A shipment of books and a package

• A savings plan with a gift card

• A gym membership fee

In the scenario where Leon saves $5 weekly with an initial $50 gift card, what is the equation to find out how many weeks it takes to save $120?

• 5x - 50 = 120

• 120 - 5x = 50

• 50x + 5 = 120

• 5x + 50 = 120

How can the equation 10x + 40 = 100 be interpreted in a real-world context?

• Purchasing books and a package

• Buying movie tickets and snacks

• Saving money with a gift card

• Paying for a gym membership

What is the significance of the number 5 in the equation 5x + 50 = 120?

• It represents the weight of each book

• It is the cost of each movie ticket

• It is the monthly gym fee

• It is the weekly savings amount