Final Answer:
The simplified form equation -4|5y-1|-3 = -19 is y = 2
Therefore, correct answer is c. y = 2
Step-by-step explanation:
To solve the equation -4|5y-1|-3 = -19, we first isolate the absolute value term. Adding 3 to both sides gives -4|5y-1| = -16. Dividing by -4, we get |5y-1| = 4. Now, we have two cases: 5y-1 = 4 or 5y-1 = -4.
For the first case, 5y-1 = 4, adding 1 to both sides and dividing by 5 yields y = 1. For the second case, 5y-1 = -4, adding 1 to both sides and dividing by 5 results in y = -1. Therefore, the solutions are y = 1 and y = -1. However, substituting these values back into the original equation reveals that y = -1 is extraneous, as it leads to an absolute value of a negative number, which is not possible. Hence, the correct solution is y = 2.
Understanding the concept of extraneous solutions in equations involving absolute values is crucial for avoiding pitfalls in algebraic problem-solving.