Question

Four students, Abbey, Jim, Mike, and Beth, were shown a set of steps that were used to solve the equation, 2(x−4)2−5=13 . The students were then asked to determine the missing step, step 3. The students were shown the information below. Equation: 2(x−4)2−5=13 . Step 1: 2(x−4)2=18 Step 2: (x−4)2=9 Step 3: ? Step 4: x−4=±3 Step 5: x=7,x=1 Each student made a claim about step 3 as shown in the table below.

Answer 1

Jim's claim is correct (B). Step 3 involves taking the square root of both sides, leading to
`\(√((x - 4)^2) = √(9)\)`. This aligns with Jim's claim, reflecting accurate mathematical reasoning in the solution process.

Let's analyze the claims:

Abbey's Claim (A):

`\[ (√(x - 4))^2 = √(9) \]`

Jim's Claim (B):

`\[ √((x - 4)^2) = √(9) \]`

Mike's Claim (C):

`\[ (x - 4)^2 + 4 = 9 + 4 \]`

Beth's Claim (D):

`\[ x - √(4) = √(9) \]`

Comparing these claims to the given steps, we can see that Jim's claim is correct. Thus, the correct answer is:

B. Jim's claim is correct.

The complete question is:
Four students, Abbey, Jim, Mike, and Beth, were shown a set of steps that were used to solve the equation, 2(x-4)2-5=13. The students were then asked to determine the missing step, step 3. The students were shown the information below. Equation: 2(x-4)^2-5=13.

Step 1:2(x-4)^2=18

Step 2: (x-4)^2=9

Step 3 : ?

Step 4: x-4=± 3

Step 5: x=7,x=1

Each student made a claim about step 3 as shown in the table below.

Which student's claim is correct?

A. Abbey's claim is correct.

B. Jim's claim is correct.

C. Mike's claim is correct.

D. Beth's claim is correct.