Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value
Absolute value represents the distance of a number from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|, and is always non-negative. For example, |3| = 3 and |-3| = 3. Understanding absolute value is crucial for solving equations and inequalities that involve it.
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Inequalities
Inequalities express a relationship between two expressions that are not necessarily equal. They can be strict (using < or >) or non-strict (using ≤ or ≥). In this case, the inequality |1.5x - 14| < 0 indicates that we are looking for values of x that make the expression less than zero, which is impossible for absolute values.
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No Solution Concept
In the context of inequalities involving absolute values, a situation may arise where no solution exists. Since absolute values are always non-negative, the inequality |1.5x - 14| < 0 cannot be satisfied by any real number. Recognizing when an equation or inequality has no solution is an important aspect of algebraic problem-solving.
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