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Sophia determined that the expression Negative (4 x minus 5) + 2 (x minus 3) is equivalent to –2x – 5 by using the steps below.


Expression: Negative (4 x minus 5) + 2 (x minus 3)
Expression: –2x – 5
Step 1:
Choose a value of x
Choose x = 1.
Choose x = negative 1.
Step 2: Substitute
Negative (4 (1) minus 5) + 2 (1 minus 3)
Negative 2 (negative 1) minus 5
Step 3: Evaluate
Negative (4 (1) minus 5) + 2 (1 minus 3) = negative (negative 1) + 2 (negative 2) = negative 3
Negative 2 (negative 1) minus 5 = 2 minus 5 = negative 3
Step 4:
Compare
Since –3 = –3, the two expressions are equivalent.

Which explains whether Sophia is correct?
She is correct because the value of the two expressions are the same in Step 3.
She is correct because she substituted opposite values in Step 1.
She is not correct because she did not substitute the same number in both expressions in Step 1.
She is not correct because she did not perform the correct order of operations in Step 3.

Respuesta :

facundo3141592

The correct statement is:

"She is not correct because she did not substitute the same number in both expressions in Step 1."

Is Sophia correct?

First, let's see if Sophia is correct.

She starts with the expression:

-(4x - 5) + 2*(x - 3) = -2x - 5

Expanding the left side:

-4x + 5 + 2x - 6 = -2x - 5

-2x -1 = -2x - 5

So the constant term is different.

Now, what Sophia does is evaluating in x = 1 and x = -1. You can't do that when finding equivalent expressions. (never evaluate in different numbers).

"She is not correct because she did not substitute the same number in both expressions in Step 1."

If you want to learn more about equivalent expressions:

https://brainly.com/question/2972832

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