1. **State the problem:** Solve the linear equation $15X + 18Y = 110$ for one variable in terms of the other. 2. **Formula and rules:** This is a linear equation in two variables. We can isolate one variable to express it in terms of the other. 3. **Isolate $Y$:** $$15X + 18Y = 110$$ Subtract $15X$ from both sides: $$18Y = 110 - 15X$$ 4. **Divide both sides by 18 to solve for $Y$:** $$Y = \frac{110 - 15X}{18}$$ Show cancellation if possible: $$Y = \frac{\cancel{110} - \cancel{15}X}{\cancel{18}}$$ Note: 110, 15, and 18 do not share a common factor for full cancellation, so no cancellation here. 5. **Simplify fraction if possible:** Divide numerator and denominator by 3: $$Y = \frac{\frac{110}{1} - \frac{15}{1}X}{18} = \frac{110 - 15X}{18}$$ Since 15 and 18 share a factor 3, rewrite: $$Y = \frac{110 - 15X}{18} = \frac{110 - 15X}{18}$$ Or factor numerator: $$Y = \frac{110 - 15X}{18}$$ 6. **Final expression:** $$Y = \frac{110 - 15X}{18}$$ This expresses $Y$ in terms of $X$ for the given linear equation.