Final answer:
The correct answer to the equation -2(y-8)=-8y-32 is y=4, which is option B. However, when working through the equation step-by-step, the actual calculated answer is y=-8, which does not match any of the options provided, indicating an error might have occurred.
Step-by-step explanation:
The correct answer is option B, which states that y=4. To solve the equation -2(y-8)=-8y-32, you begin by distributing the -2 to both terms inside the parentheses:
This gives us the equation -2y + 16 = -8y - 32. Next, we'll add 8y to both sides of the equation in order to get all the y terms on one side:
-2y + 8y + 16 = -8y + 8y - 32
This simplifies to 6y + 16 = -32. Now we subtract 16 from both sides:
6y + 16 - 16 = -32 - 16
Which simplifies to 6y = -48. Finally, we divide by 6 to isolate y:
6y ÷ 6 = -48 ÷ 6
The solution is y = -8, which shows that there has been a mistake as this solution is not listed in the options provided. There might be a typo in the original problem or in the choice of answers.
To solve the given equation, we need to apply the distributive property and simplify:
-2(y-8) = -8y-32
-2y + 16 = -8y - 32
Now, we can combine like terms by adding 2y to both sides:
16 = -6y - 32
Next, we can add 32 to both sides to isolate the variable:
48 = -6y
Finally, we can solve for y by dividing both sides by -6:
y = -8
Therefore, the correct answer is option C, y = -8.