1. **State the problem:** We are given the equation $c=\frac{3x}{2x-11}$ and need to make $x$ the subject. 2. **Write the equation:** $$c=\frac{3x}{2x-11}$$ 3. **Multiply both sides by the denominator to eliminate the fraction:** $$c(2x-11)=3x$$ 4. **Distribute $c$ on the left side:** $$2cx - 11c = 3x$$ 5. **Group all terms involving $x$ on one side:** $$2cx - 3x = 11c$$ 6. **Factor out $x$ on the left side:** $$x(2c - 3) = 11c$$ 7. **Divide both sides by $(2c - 3)$ to isolate $x$:** $$x = \frac{11c}{2c - 3}$$ **Final answer:** $$x = \frac{11c}{2c - 3}$$ This formula expresses $x$ in terms of $c$.