\( \frac{a}{-2}<-1 \) or \( -4 a+3 \geq 23 \) Solution Interval Notation \( \square \)

To solve \( \frac{a}{-2} < -1 \), multiply both sides by -2 (note that this reverses the inequality), giving \( a > 2 \). For the second inequality \( -4a + 3 \geq 23 \), subtract 3 from both sides to get \( -4a \geq 20 \). Dividing by -4 (again reversing the inequality) gives \( a \leq -5 \). Combining these results, the solution in interval notation is: \( (-\infty, -5] \cup (2, \infty) \). If you find inequalities confusing, remember that reversing the inequality is like flipping a pancake: when you do it, things get turned upside down! Common mistakes often arise from forgetting this crucial step. Always be cautious about signs when multiplying or dividing negative numbers!