\(\dfrac{1}{4}x-\dfrac{1}{8}=\dfrac{7}{8}+\dfrac{1}{2}x\ \ \ \ |multiply\ both\ sides\ by\ 8\\\\8\cdot\dfrac{1}{4}x-8\cdot\dfrac{1}{8}=8\cdot\dfrac{7}{8}+8\cdot\dfrac{1}{2}x\\\\2x-1=7+4x\ \ \ |add\ 1\ to\ both\ sides\\\\2x=8+4x\ \ \ \ |subtract\ 4x\ from\ both\ sides\\\\-2x=8\ \ \ \ |divide\ both\ sides\ by\ (-2)\\\\\boxed{x=-4}\)
