Solve for t. 3t-15lt -3 and -4tlt 12 -6lt tlt -3 tlt -3 4lt tlt -3 -3lt tlt 4

To solve the system of inequalities, we need to solve each inequality separately and then find the intersection of the solutions.<br /><br />1. Solving the first inequality:<br />$3t-15\lt -3$<br />Add 15 to both sides:<br />$3t\lt 12$<br />Divide both sides by 3:<br />$t\lt 4$<br /><br />2. Solving the second inequality:<br />$-4t\lt 12$<br />Divide both sides by -4 (and reverse the inequality sign):<br />$t\gt -3$<br /><br />Now, we need to find the intersection of the solutions for both inequalities. The solution for the first inequality is $t\lt 4$, and the solution for the second inequality is $t\gt -3$. Therefore, the intersection of the solutions is $-3\lt t\lt 4$.<br /><br />So, the correct answer is $-3\lt t\lt 4$.