1. **State the problem:** Solve the equation $1.6x + 1.475(1 - x) = 1.50974$ for $x$. 2. **Write the equation and apply distributive property:** $$1.6x + 1.475 - 1.475x = 1.50974$$ 3. **Combine like terms:** $$ (1.6x - 1.475x) + 1.475 = 1.50974$$ $$0.125x + 1.475 = 1.50974$$ 4. **Isolate the variable term:** $$0.125x = 1.50974 - 1.475$$ $$0.125x = 0.03474$$ 5. **Solve for $x$ by dividing both sides by 0.125:** $$x = \frac{0.03474}{0.125}$$ $$x = 0.27792$$ **Final answer:** $$x = 0.27792$$