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Let’s explore beginning with the first inequality: To solve , you can treat it as two separate inequalities. Start with by adding 3 to both sides, giving you , and then divide by -3 (remember to reverse the inequality sign), leading to . Now for the second part, , add 3 to get , and dividing by -3 gives . So, combining these results, we find that .

Now, diving into the second inequality: To tackle , we multiply everything by -6 (switching those inequality signs!). So we have . From the first part, subtracting 3 gives us , leading to . In the second part, gives . Therefore, combining this gives .

Now for the last one: Also set as two inequalities, from , we multiply by -2, which alters the signs. This gives us . Solving the first part, subtracting 5 results in , yielding . On the other end, leads to . Hence, we can combine this to find that .

Now that’s one wild ride through inequalities! Keep those signs in check, and you’re on a mathematical adventure!