Final answer:
Compound inequalities using "and" require both conditions to be met, creating an intersection of solutions, while "or" allows either condition to be met, creating a union of solutions. Solving involves isolating the variable and combining solutions accordingly.
Step-by-step explanation:
When solving compound inequalities using "and" and "or," it's important to understand that each word indicates a different type of relationship between the inequalities. An "and" compound inequality means both conditions must be met simultaneously; the solution is the intersection of the two individual inequalities. On the other hand, an "or" compound inequality means that the solution can satisfy either one of the inequalities; this is represented by the union of the individual solutions.
For example, the inequality 3 < x < 7 is an "and" situation because x must be both greater than 3 and less than 7 at the same time. On the contrary, x < 3 or x > 7 indicates that x can be either less than 3 or greater than 7, encompassing a broader range of possible values.
To solve these inequalities, one typically isolates the variable on one side of each inequality and then combines the separate solutions in a way that reflects the logical connection implied by "and" or "or." It's essential to maintain the integrity of the inequality by performing the same operations on both sides of the equation, and if multiplying or dividing by a negative number, to remember to reverse the inequality symbol.