#### Answer

$t=5$

#### Work Step by Step

Step 1: $\frac{t-4}{2}-\frac{t-3}{9}=\frac{5}{18}$
Step 2: $\frac{9(t-4)-2(t-3)}{18}=\frac{5}{18}$
Step 3: $\frac{9t-36-2t+6}{18}=\frac{5}{18}$
Step 4: $\frac{7t-30}{18}=\frac{5}{18}$
Step 5: $18(7t-30)=5(18)$
Step 6: $7t-30=5$
Step 7: $7t=5+30$
Step 8: $7t=35$
Step 9: $t=5$