Solve each equation or inequality. | 1.5x - 14| < 0

Verified step by step guidance

1. Understand that the expression \(|1.5x - 14| < 0\) involves an absolute value inequality.
2. Recall that the absolute value of any real number is always non-negative, meaning it is always greater than or equal to zero.
3. Since the absolute value \(|1.5x - 14|\) is always non-negative, it cannot be less than zero.
4. Conclude that there are no real solutions to the inequality \(|1.5x - 14| < 0\) because an absolute value cannot be negative.
5. Therefore, the solution set is empty, indicating no values of \(x\) satisfy the inequality.

Key Concepts

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.

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.

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.