1. **State the problem:** Solve the equation $\frac{15}{27} = \frac{2x}{x+26}$ for $x$. 2. **Write the equation:** $$\frac{15}{27} = \frac{2x}{x+26}$$ 3. **Cross multiply to eliminate the fractions:** $$15(x+26) = 27(2x)$$ 4. **Expand both sides:** $$15x + 390 = 54x$$ 5. **Bring all terms involving $x$ to one side:** $$15x + 390 = 54x \implies 390 = 54x - 15x$$ 6. **Simplify the right side:** $$390 = 39x$$ 7. **Divide both sides by 39 to solve for $x$:** $$x = \frac{390}{39}$$ 8. **Simplify the fraction:** $$x = \cancel{\frac{390}{39}} = 10$$ **Final answer:** $$x = 10$$