Table of contents

0. Review of Algebra4h 16m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 19m
10. Combinatorics & Probability1h 45m

1. Equations & Inequalities

Linear Inequalities

College Algebra

1. Equations & Inequalities

Linear Inequalities

0:39 minutes

Problem 62a

Textbook Question

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

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Key Concepts

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.

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.