Verified answer

[tex] \frac{3}{4} (8t + 1) < \frac{5}{6} (16t - 3) - 12 \frac{1}{2} \\ 6t + \frac{3}{4} < \frac{40}{3} t - \frac{5}{2} - \frac{25}{2} \\ 6t - \frac{40}{3} t < - \frac{5}{2} - \frac{25}{2} - \frac{3}{4} \\ \frac{18 - 40}{3} t < \frac{ - 10 - 50 - 3}{4} \\ - \frac{22}{3} t < - \frac{63}{4} \\ t > \frac{63}{4} \times \frac{3}{22} \\ t > \frac{189}{88} \\ t > 2 \frac{13}{88} [/tex]