Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|. For example, |3| = 3 and |-3| = 3. In equations and inequalities, absolute values can create two separate cases to consider, as they can be either positive or negative.
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Inequalities
Inequalities express a relationship where one side is not equal to the other, using symbols like <, >, ≤, or ≥. They indicate that one quantity is less than or greater than another. Solving inequalities often involves similar steps to solving equations, but requires careful consideration of the direction of the inequality when multiplying or dividing by negative numbers.
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Solving Compound Inequalities
Compound inequalities involve two or more inequalities that are connected by 'and' or 'or'. To solve them, one must find the values that satisfy all parts of the inequality. In the context of absolute value inequalities, this often leads to breaking the problem into two separate cases, allowing for a comprehensive solution that encompasses all possible scenarios.
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