1. **State the problem:** We are given the equation $$2(kx - n) = - \frac{28}{15} x - \frac{36}{19}$$ where $k$ and $n$ are constants and $n > 1$. The equation has no solution. We need to find the value of $k$. 2. **Rewrite the equation:** Distribute the 2 on the left side: $$2kx - 2n = - \frac{28}{15} x - \frac{36}{19}$$ 3. **Group like terms:** Bring all terms involving $x$ to one side and constants to the other: $$2kx + \frac{28}{15} x = 2n - \frac{36}{19}$$ 4. **Factor out $x$ on the left:** $$x \left(2k + \frac{28}{15}\right) = 2n - \frac{36}{19}$$ 5. **Analyze the condition for no solution:** An equation of the form $Ax = B$ has no solution if and only if $A = 0$ but $B \neq 0$. So, for no solution: $$2k + \frac{28}{15} = 0$$ and $$2n - \frac{36}{19} \neq 0$$ 6. **Solve for $k$:** $$2k = - \frac{28}{15}$$ $$k = - \frac{28}{15} \times \frac{1}{2} = - \frac{28}{30} = - \frac{14}{15}$$ 7. **Check the condition on $n$:** Since $n > 1$, check if $2n - \frac{36}{19} \neq 0$: $$2n - \frac{36}{19} > 2(1) - \frac{36}{19} = 2 - 1.8947 = 0.1053 \neq 0$$ So the condition holds. **Final answer:** $$\boxed{k = - \frac{14}{15}}$$