Final answer:
No student is correct; the equation -2.5(5 - 7) + 2 = 15 is not solved correctly by any of them. The correct solution should follow the order of operations, resulting in a value of 7, not 15.
Step-by-step explanation:
To solve the equation -2.5(5 - 7) + 2 = 15, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Starting with the expression within the parentheses (5 - 7), we subtract 7 from 5, which results in -2. Now, we multiply -2.5 by -2. This multiplication of two negative numbers results in a positive product, namely 5. We then add this to 2, getting 7 as our intermediate result. Now, we compare it to the right side of the original equation (15), and it is clear that 7 does not equal 15. Therefore, the equation -2.5(5 - 7) + 2 = 15 is incorrect as solved.
Let's go through the step-by-step solution:
- Calculate the expression within parentheses: 5 - 7 = -2.
- Multiply by -2.5: -2.5 x (-2) = 5.
- Add 2 to the product: 5 + 2 = 7.
- Compare the result with 15: 7 is not equal to 15.
This means that none of the students, Shawna, Dexter, or Tilana, are correct if they claim the equation equals 15.