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 Equations

College Algebra

1. Equations & Inequalities

Linear Equations

1:28 minutes

Problem 8

Textbook Question

Decide whether each statement is true or false. The equation 5x=4x is an example of a contradiction.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equations and Solutions

An equation is a mathematical statement that asserts the equality of two expressions. To solve an equation, we find the value(s) of the variable that make the equation true. In the case of 5x = 4x, we can simplify it to x = 0, indicating that there is a solution rather than a contradiction.

Contradiction in Mathematics

A contradiction occurs when a statement is proven to be false under all circumstances. In algebra, an example of a contradiction would be an equation that simplifies to a false statement, such as 0 = 5. The equation 5x = 4x does not meet this criterion, as it has a valid solution.

Simplifying Equations

Simplifying an equation involves manipulating it to make it easier to solve or understand. This can include combining like terms, isolating variables, or performing operations on both sides. For 5x = 4x, subtracting 4x from both sides leads to x = 0, demonstrating that the equation is not a contradiction.