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Ch. 2-4 continued

This lesson covers the comparison of truck rental costs between Ace Truck Rental and Roni's Truck Rental. Ace charges $54 per day plus $0.09 per mile, while Roni's charges $38 per day plus $0.13 per mile. The goal is to determine the number of miles for which the costs are equal. Additionally, the lesson explores identities in equations that yield true statements for all values of the variable, and scenarios where equations have no solution, providing examples and practice problems for better understanding.

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Ch. 2-4 continued

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  1. Ch. 2-4 continued

  2. POD • Solve: 2y=3y-20 • Ace Truck Rental charges $54 a day plus $.09 per mile. Roni’s Truck Rental charges $38 a day plus $.13 per mile. For how many miles will the cost of renting a truck for one day at Ace equal the cost at Roni’s?

  3. Identities & Equations with no solutions • Identity: an equation that is true for every value of the variable - example: 2x = 2x Solve: 10-8a = 2(5-4a) 10-8a = 2(5-4a) 10-8a = 10 – 8a +8a +8a 10 = 10 This is always true! Therefore it is an identity!

  4. Example 2 8z-7=3z-7+5z 8z-7=8z-7 -8z -8z -7=-7 Combine like terms

  5. Practice • 4(b-1)=-4+4b • 6y+9=3(2y+3)

  6. When we have no solution… 6m – 5 = 7m+7-m 6m -5 = 6m +7 -6m -6m -5 = 7 Combine like terms -5 ≠ 7 therefore I have no solution

  7. Example 2 Combine like terms 3(n-1) = 5n +3 -2n 3n -3 = 3n +3 -3n -3n -3 = 3 -3 ≠ 3 No Solution

  8. Practice • 8(2f-3) = 4(4f-8) • 3(2f+4) = 2(3f -6)

  9. Homework • Page 99 #’s 22-39

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