1. **Problem 1:** Solve the equation $4x + 5(2x - 7) = 7$. 2. Expand the expression: $$4x + 5(2x - 7) = 4x + 10x - 35$$ 3. Combine like terms: $$4x + 10x - 35 = 14x - 35$$ 4. Set the equation equal to 7: $$14x - 35 = 7$$ 5. Add 35 to both sides: $$14x = 7 + 35 = 42$$ 6. Divide both sides by 14: $$x = \frac{42}{14} = 3$$ --- 7. **Problem 2:** Triangle ABC is isosceles with perpendicular height from B to AC equal to 12 cm and angle $\angle ACB = 72^\circ$. Find the length $AC$. 8. Since triangle ABC is isosceles with $AB = BC$, the height from B to AC bisects AC and angle $\angle ACB$. 9. The base AC is split into two equal segments, each of length $\frac{AC}{2}$. 10. The height forms a right triangle with hypotenuse $BC$ and one leg 12 cm. 11. The angle at C is $72^\circ$, so each half of the base corresponds to an angle of $36^\circ$. 12. Using right triangle trigonometry, the half base is: $$\frac{AC}{2} = 12 \times \tan(36^\circ)$$ 13. Calculate $\tan(36^\circ)$ (approximate): $$\tan(36^\circ) \approx 0.7265$$ 14. Compute half base: $$\frac{AC}{2} = 12 \times 0.7265 = 8.718$$ 15. Therefore, full base length: $$AC = 2 \times 8.718 = 17.436$$ 16. Rounded to sensible accuracy: $$AC \approx 17.4 \text{ cm}$$