1. **State the problem:** Solve the equation $x - 3 = 5x + 7$ and check the solution. 2. **Formula and rules:** To solve linear equations, isolate the variable on one side by performing inverse operations (addition, subtraction, multiplication, division) equally on both sides. 3. **Step-by-step solution:** 1. Start with the equation: $$x - 3 = 5x + 7$$ 2. Subtract $x$ from both sides to get variables on one side: $$x - 3 - x = 5x + 7 - x$$ $$-3 = 4x + 7$$ 3. Subtract 7 from both sides to isolate the term with $x$: $$-3 - 7 = 4x + 7 - 7$$ $$-10 = 4x$$ 4. Divide both sides by 4 to solve for $x$: $$x = \frac{-10}{4} = -\frac{5}{2}$$ 4. **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:** $$x = -\frac{5}{2}$$