1. **State the problem:** Solve the equation $x - 10 + 7x = 15 + 3x$ for $x$. 2. **Combine like terms on each side:** On the left side, combine $x$ and $7x$: $$x + 7x = 8x$$ So the equation becomes: $$8x - 10 = 15 + 3x$$ 3. **Isolate variable terms on one side:** Subtract $3x$ from both sides: $$8x - 10 - 3x = 15 + 3x - 3x$$ $$\cancel{8x} + \cancel{-3x} - 10 = 15 + \cancel{3x} - \cancel{3x}$$ $$5x - 10 = 15$$ 4. **Isolate the term with $x$:** Add 10 to both sides: $$5x - 10 + 10 = 15 + 10$$ $$5x = 25$$ 5. **Solve for $x$ by dividing both sides by 5:** $$\frac{5x}{\cancel{5}} = \frac{25}{\cancel{5}}$$ $$x = 5$$ **Final answer:** $$x = 5$$