1. **State the problem:** Solve the equation $7 - 2x = 5x + 14$ for $x$. 2. **Write down the formula and rules:** To solve linear equations, we isolate the variable on one side by performing the same operation on both sides. 3. **Step 1: Move all $x$ terms to one side.** Add $2x$ to both sides: $$7 = 5x + 14 + 2x$$ which simplifies to $$7 = 7x + 14$$ 4. **Step 2: Move constants to the other side.** Subtract $14$ from both sides: $$7 - 14 = 7x$$ which simplifies to $$-7 = 7x$$ 5. **Step 3: Solve for $x$.** Divide both sides by $7$: $$x = \frac{-7}{7} = -1$$ 6. **Final answer:** $x = -1$