Question

Sophia determined that the expression negative (4 x - 5) +2 (x - 3) is equivalent to –2x – 5 by using the steps below. expression: - (4 x - 5) + 2 (x - 3) expression: –2x – 5 step 1: choose a value of x choose x = 1 choose x = -1 step 2: substitute -(4 (1) - 5) + 2 (1 - 3) -2 (-1) - 5 step 3: evaluate -(4 (1) - 5) + 2 (1 - 3) = -(1) + 2 (-2) = -3 -2 (-1) - 5 = 2 - 5 = -3 step 4: compare since –3 = –3, the two expressions are equivalent. which explains whether sophia is correct? a. she is correct because the value of the two expressions are the same in step 3. b. she is correct because she substituted opposite values in step 1. c. she is not correct because she did not substitute the same number in both expressions in step 1. d. she is not correct because she did not perform the correct order of operations in step 3.

Answer 1

Sophia's conclusion that the expressions are equivalent is incorrect because she did not use the correct order of operations in her calculations. As a result, her evaluation of the expressions led to different values, indicating that the expressions are not equivalent.

Step-by-step explanation:

Sophia's approach to determining whether the expressions negative (4x - 5) +2 (x - 3) and −2x - 5 are equivalent is not entirely correct. The steps she took of choosing a value for x and substituting those values into the expressions is valid, but her calculations in step 3 are incorrect. To correctly evaluate the expressions, she would need to perform the operations in the correct order, known as the order of operations, or PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

For example, in the expression negative (4x - 5) +2 (x - 3), if x is 1, the correct evaluation should be -(4*1 - 5) + 2 *(1-3) = -(4 - 5) + 2*(-2) = -1 - 4 = -5, not -3 as Sophia calculated. Therefore, the correct assessment in step 4 is not true; Sophia's calculation of both expressions resulted in different values, indicating that the two expressions are not equivalent. So, the answer is D. She is not correct because she did not perform the correct order of operations in step 3.

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