1. **State the problem:** Solve the inequality $4x(x) - 25 + 3(x-1) > 4x(x-4) + 15$. 2. **Rewrite the inequality:** $$4x^2 - 25 + 3x - 3 > 4x^2 - 16x + 15$$ 3. **Simplify both sides:** Left side: $4x^2 + 3x - 28$ Right side: $4x^2 - 16x + 15$ 4. **Bring all terms to one side:** $$4x^2 + 3x - 28 - (4x^2 - 16x + 15) > 0$$ 5. **Distribute the minus sign:** $$4x^2 + 3x - 28 - 4x^2 + 16x - 15 > 0$$ 6. **Combine like terms:** $$ (4x^2 - 4x^2) + (3x + 16x) + (-28 - 15) > 0$$ $$0 + 19x - 43 > 0$$ 7. **Simplify:** $$19x - 43 > 0$$ 8. **Isolate $x$:** $$19x > 43$$ 9. **Divide both sides by 19:** $$\cancel{19}x > \cancel{19} \frac{43}{19}$$ $$x > \frac{43}{19}$$ 10. **Final answer:** $$x > \frac{43}{19}$$ This means all values of $x$ greater than $\frac{43}{19}$ satisfy the inequality.