1. **State the problem:** Solve the equation $$4(x+10) = 10x$$ for $$x$$. 2. **Apply the distributive property:** Multiply 4 by each term inside the parentheses. $$4(x+10) = 4 \times x + 4 \times 10 = 4x + 40$$ 3. **Rewrite the equation:** $$4x + 40 = 10x$$ 4. **Isolate the variable terms on one side:** Subtract $$4x$$ from both sides. $$\cancel{4x} + 40 = 10x - \cancel{4x}$$ $$40 = 6x$$ 5. **Solve for $$x$$:** Divide both sides by 6. $$\frac{40}{\cancel{6}} = \frac{6x}{\cancel{6}}$$ $$\frac{40}{6} = x$$ 6. **Simplify the fraction:** $$x = \frac{20}{3}$$ **Final answer:** $$x = \frac{20}{3}$$