Where to use intersection or union in modulus inquality

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Understanding when to use intersection or union in modulus inequalities depends on the form of the inequality. For inequalities like absolute value of x less than a, we use intersection. For inequalities like absolute value of x greater than a, we use union. Let me show you why with a visual representation. Let's work through a specific example. Consider the inequality absolute value of x minus 3 less than 2. Since this is in the form absolute value of expression less than a, we use intersection. We convert it to negative 2 less than x minus 3 less than 2. Solving both parts gives us x greater than 1 and x less than 5. The intersection of these conditions is 1 less than x less than 5.