1. Stating the problem: Solve for $z$ in the equation $$\frac{7}{10} = \frac{2}{5} z$$. 2. To isolate $z$, divide both sides of the equation by $\frac{2}{5}$. 3. Dividing by a fraction is the same as multiplying by its reciprocal, so: $$z = \frac{\frac{7}{10}}{\frac{2}{5}} = \frac{7}{10} \times \frac{5}{2}$$ 4. Multiply the numerators and denominators: $$z = \frac{7 \times 5}{10 \times 2} = \frac{35}{20}$$ 5. Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 5: $$z = \frac{\cancel{35}^{\,7}}{\cancel{20}^{\,4}} = \frac{7}{4}$$ 6. Final answer: $$z = \frac{7}{4}$$