Final answer:
To solve the equation |4x - 2| - 14 = 0, isolate the absolute value expression and split the equation into two cases. Solving these cases gives x = 4 and x = -3.
Step-by-step explanation:
To solve the equation |4x - 2| - 14 = 0, we first isolate the absolute value expression by adding 14 to both sides: |4x - 2| = 14.
Then, we can split the equation into two cases based on the positive and negative values of the absolute value: 4x - 2 = 14 or 4x - 2 = -14.
Solving these linear equations gives us x = 4 and x = -3.