d. \( \frac{1}{2}-\frac{1}{3}=1-\frac{5}{8} x \)

To solve the equation \[ \frac{1}{2} - \frac{1}{3} = 1 - \frac{5}{8} x, \] we first simplify the left side. To do this, we need a common denominator for \(\frac{1}{2}\) and \(\frac{1}{3}\). The least common multiple of 2 and 3 is 6. Rewriting the fractions with a common denominator: \[ \frac{1}{2} = \frac{3}{6}, \quad \frac{1}{3} = \frac{2}{6}. \] Now we can subtract: \[ \frac{3}{6} - \frac{2}{6} = \frac{1}{6}. \] So the equation now looks like: \[ \frac{1}{6} = 1 - \frac{5}{8} x. \] Next, we isolate \(-\frac{5}{8} x\) by subtracting 1 from both sides: \[ \frac{1}{6} - 1 = -\frac{5}{8} x. \] To combine \(\frac{1}{6}\) and \(-1\), we rewrite \(-1\) as \(-\frac{6}{6}\): \[ \frac{1}{6} - \frac{6}{6} = -\frac{5}{6}. \] Now we have: \[ -\frac{5}{6} = -\frac{5}{8} x. \] To eliminate the negative signs, we can multiply both sides by -1: \[ \frac{5}{6} = \frac{5}{8} x. \] Next, we can solve for \(x\) by dividing both sides by \(\frac{5}{8}\): \[ x = \frac{5/6}{5/8}. \] Dividing by a fraction is the same as multiplying by its reciprocal: \[ x = \frac{5}{6} \cdot \frac{8}{5}. \] The \(5\)s cancel out: \[ x = \frac{8}{6} = \frac{4}{3}. \] Thus, the solution is: \[ \boxed{\frac{4}{3}}. \]