1. The problem involves the expression $k_1 = \frac{x}{4}$ and the equation $\frac{x}{4} u1.5h + x = \frac{x}{\frac{x}{2}} u1.5, 8x$. 2. We first clarify each part: $k_1 = \frac{x}{4}$ is a definition. 3. In the equation, interpret terms carefully: $\frac{x}{4} u1.5h$ likely means $\frac{x}{4} \times 1.5h = \frac{3xh}{8}$. 4. The right side $\frac{x}{\frac{x}{2}} u1.5$ simplifies as $\frac{x}{\frac{x}{2}} = 2$ (since $x \neq 0$), so multiplying by $1.5$ gives $3$. 5. The term $8x$ is standalone; so the right side is $3, 8x$ possibly meaning $3 + 8x$ or a sequence. Assuming addition, right side is $3 + 8x$. 6. Rewrite the full equation as $\frac{3xh}{8} + x = 3 + 8x$. 7. Combine like terms: bring $x$ terms to one side: $\frac{3xh}{8} + x - 8x = 3$. 8. Simplify $x - 8x = -7x$: $\frac{3xh}{8} - 7x = 3$. 9. Factor out $x$: $x\left( \frac{3h}{8} - 7 \right) = 3$. 10. Solve for $x$: $$x = \frac{3}{\frac{3h}{8} - 7} = \frac{3}{\frac{3h - 56}{8}} = \frac{3 \times 8}{3h - 56} = \frac{24}{3h - 56}.$$ Final answer: $$x = \frac{24}{3h - 56}.$$