After evaluating both expressions for x values of 1, 2, and 3, we find that the results are the same, confirming that the expressions 3.25(x - 5) and 3.25x - 16.25 are equivalent due to the Distributive Property.
Step-by-step explanation:
To determine if the expressions 3.25(x - 5) and 3.25x - 16.25 are equivalent, we evaluate both expressions for the same values of x and compare the results. We'll complete the table for each x value of 1, 2, and 3:
For x=1: 3.25(1 - 5) = 3.25 * (-4) = -13; 3.25 * 1 - 16.25 = 3.25 - 16.25 = -13
For x=2: 3.25(2 - 5) = 3.25 * (-3) = -9.75; 3.25 * 2 - 16.25 = 6.5 - 16.25 = -9.75
For x=3: 3.25(3 - 5) = 3.25 * (-2) = -6.5; 3.25 * 3 - 16.25 = 9.75 - 16.25 = -6.5
The results are the same for both expressions, thus confirming they are equivalent. This is an example of the Distributive Property, which states that a(b + c) = ab + ac.