I. \( 2>-3-3 x \geq-7 \) m. n. \( -4<\frac{5 x+3}{-6} \leq 2 \) o. \( -4 \leq \frac{5+3 x}{-2} \leq 5 \)

Let’s explore beginning with the first inequality: To solve \( 2 > -3 - 3x \geq -7 \), you can treat it as two separate inequalities. Start with \( 2 > -3 - 3x \) by adding 3 to both sides, giving you \( 5 > -3x \), and then divide by -3 (remember to reverse the inequality sign), leading to \( x > -\frac{5}{3} \). Now for the second part, \(-3 - 3x \geq -7\), add 3 to get \(-3x \geq -4\), and dividing by -3 gives \( x \leq \frac{4}{3} \). So, combining these results, we find that \( -\frac{5}{3} < x \leq \frac{4}{3}\). Now, diving into the second inequality: To tackle \(-4 < \frac{5x + 3}{-6} \leq 2\), we multiply everything by -6 (switching those inequality signs!). So we have \( 24 > 5x + 3 \geq -12 \). From the first part, subtracting 3 gives us \( 21 > 5x \), leading to \( x < \frac{21}{5} \). In the second part, \( 5x \geq -15 \) gives \( x \geq -3 \). Therefore, combining this gives \( -3 \leq x < \frac{21}{5} \). Now for the last one: Also set as two inequalities, from \(-4 \leq \frac{5 + 3x}{-2} \leq 5\), we multiply by -2, which alters the signs. This gives us \( 8 \geq 5 + 3x \geq -10\). Solving the first part, subtracting 5 results in \( 3 \geq 3x \), yielding \( 1 \geq x \). On the other end, \( 3x \geq -15\) leads to \( x \geq -5\). Hence, we can combine this to find that \( -5 \leq x \leq 1\). Now that’s one wild ride through inequalities! Keep those signs in check, and you’re on a mathematical adventure!