Question

Write explain how to determine whether an absolute value inequality uses a compound inequality with and or a compound equality with or. then summarize how to solve absolute value inequalities.

Answer 1

To determine the correct compound inequality for an absolute value inequality, identify if the initial inequality is < (and) or > (or). Then, solve each corresponding inequality separately, and check your answer for reasonableness.

Step-by-step explanation:

To determine whether an absolute value inequality uses a compound inequality with and or or, first consider the format of the inequality. If the inequality is written as |x| < a, this translates to a compound inequality of x > -a and x < a. In contrast, if the inequality is written as |x| > a, this translates to a compound inequality of x < -a or x > a.

To solve absolute value inequalities, follow these steps:

1. Write the absolute value inequality as two separate inequalities based on the initial comparison (whether it's < a or > a).
2. Solve each inequality individually, treating the absolute value expression like a regular variable.
3. Combine the solutions in a manner consistent with the inequalities being and or or.
4. Check your answer to ensure it makes sense within the context of the question.