1. **State the problem:** Solve the linear equation $3x + 5 = 27$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Subtract or add terms to both sides and then divide or multiply to solve for $x$. 3. **Step-by-step solution:** - Start with the equation: $$3x + 5 = 27$$ - Subtract 5 from both sides to isolate the term with $x$: $$3x + 5 - 5 = 27 - 5$$ - Simplify: $$3x = 22$$ - Divide both sides by 3 to solve for $x$: $$x = \frac{22}{3}$$ 4. **Final answer:** $$x = \frac{22}{3}$$ or approximately $7.33$. This means the value of $x$ that satisfies the equation is $\frac{22}{3}$.