3. Solve: x-4leqslant 5 OR -3xlt -36 1 xleqslant 9 AND xlt 12 xleqslant 9 OR xgt 12 xleqslant 9 OR xlt 12 xleqslant 9 AND xgt 12

To solve the given compound inequality, we need to solve each inequality separately and then combine the solutions.<br /><br />The first inequality is $x-4\leqslant 5$. To solve for $x$, we add $4$ to both sides of the inequality:<br /><br />$x-4+4\leqslant 5+4$<br /><br />Simplifying, we get:<br /><br />$x\leqslant 9$<br /><br />The second inequality is $-3x\lt -36$. To solve for $x$, we divide both sides of the inequality by $-3$. Remember that when dividing or multiplying an inequality by a negative number, the direction of the inequality sign changes:<br /><br />$\frac{-3x}{-3}\gt \frac{-36}{-3}$<br /><br />Simplifying, we get:<br /><br />$x\gt 12$<br /><br />Now, we combine the solutions of the two inequalities. Since the compound inequality is connected by the word "OR", we take the union of the two solutions. This means that $x$ can satisfy either inequality.<br /><br />Therefore, the solution to the compound inequality is $x\leqslant 9$ OR $x\gt 12$.