1. **State the problem:** Solve the equation $7 + 9x - 18 = 1$ for $x$. 2. **Simplify the left side:** Combine like terms $7$ and $-18$. $$7 - 18 = -11$$ So the equation becomes: $$-11 + 9x = 1$$ 3. **Isolate the term with $x$:** Add $11$ to both sides to move the constant term. $$\cancel{-11} + 9x + 11 = 1 + 11$$ $$9x = 12$$ 4. **Solve for $x$:** Divide both sides by $9$. $$x = \frac{12}{9}$$ 5. **Simplify the fraction:** $$x = \frac{\cancel{12}^{4} }{\cancel{9}^{3}} = \frac{4}{3}$$ **Final answer:** $$x = \frac{4}{3}$$