Question

Vanessa tried to solve an equation step by step: −12 = 4(f - 6). She did the following steps: Step 1: −12 = 4f - 24 Step 2: 12 = 4f Step 3: 4 = f Find Vanessa's mistake. Choose the step where the mistake occurred. A. Step 1 B. Step 2 C. Step 3 D. Vanessa did not make a mistake.

Answer 1

Vanessa made a mistake in Step 2 of her calculation by incorrectly changing the sign without adjusting the right side of the equation. The correct second step is to add 24 to both sides which would make f equal to 9 after dividing both sides by 4.

Step-by-step explanation:

Vanessa made a mistake in Step 2 of solving the equation −12 = 4(f - 6). In Step 1, she correctly distributed the 4 into the parentheses to get 4f - 24. The mistake happens in Step 2, where instead of adding 24 to both sides to isolate the term 4f, she incorrectly changed the sign on the left side from negative to positive without adjusting the right side of the equation.

The correct sequence of steps should be:

• Step 1: −12 = 4f - 24 (correct distribution)
• Step 2: 12 + 24 = 4f (adding 24 to both sides)
• Step 3: 36 = 4f (combining like terms)
• Step 4: 9 = f (dividing both sides by 4)

Therefore, the correct answer should be f = 9, not f = 4 as Vanessa incorrectly concluded.