1. **State the problem:** Solve the equation $x - 3 = 5x + 7$ and check the solution. 2. **Write the equation:** $$x - 3 = 5x + 7$$ 3. **Goal:** Isolate $x$ on one side. 4. **Step 1:** Subtract $x$ from both sides to get all $x$ terms on the right: $$x - 3 - x = 5x + 7 - x \implies -3 = 4x + 7$$ 5. **Step 2:** Subtract 7 from both sides to isolate the term with $x$: $$-3 - 7 = 4x + 7 - 7 \implies -10 = 4x$$ 6. **Step 3:** Divide both sides by 4 to solve for $x$: $$x = \frac{-10}{4} = -\frac{5}{2}$$ 7. **Check the solution:** Substitute $x = -\frac{5}{2}$ back into the original equation: Left side: $$x - 3 = -\frac{5}{2} - 3 = -\frac{5}{2} - \frac{6}{2} = -\frac{11}{2}$$ Right side: $$5x + 7 = 5 \times -\frac{5}{2} + 7 = -\frac{25}{2} + \frac{14}{2} = -\frac{11}{2}$$ Both sides equal $-\frac{11}{2}$, so the solution is correct. **Final answer:** $$x = -\frac{5}{2}$$