Question

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

Answer 1

Answer:

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

Step-by-step explanation:

CASE 1: substitute 1 for x  to both sides of the equations

L.H.S

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

-(4 (1) - 5)+ 2(1-3) = - (-1) + 2(-2) = 1 - 4 = -3

R.H.S

-2x - 5

-2(1) - 5 = -2-5 = -7

Hence for x= 1

-(4x-5)+2(x-3) ≠ -2x -5

Because -3 ≠ -7

CASE 2: substitute -1 for x  to both sides of the equations

L.H.S

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

-(4 (-1) - 5)+ 2(-1-3) = - (-9) + 2(-4) = 9 - 8 = 1

R.H.S

-2x - 5

-2(-1) - 5 = 2-5 = -3

Hence for x= -1

-(4x-5)+2(x-3) ≠ -2x -5

Because 1 ≠ -3

Answer:

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

Answer 2

Answer:

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

Step-by-step explanation:

The answer is C