1. **State the problem:** Solve the linear equation $7x - 8 = 57$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate $x$ by performing inverse operations. Add or subtract terms to move constants to one side and divide to solve for $x$. 3. **Step 1:** Add 8 to both sides to cancel the $-8$ on the left: $$7x - 8 + 8 = 57 + 8$$ $$7x = 65$$ 4. **Step 2:** Divide both sides by 7 to isolate $x$: $$\frac{7x}{\cancel{7}} = \frac{65}{\cancel{7}}$$ $$x = \frac{65}{7}$$ 5. **Final answer:** $$x = \frac{65}{7}$$ This is the exact solution. You can also write it as a decimal approximately $9.29$.