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

1:19 minutes

Problem 95a

Textbook Question

Retaining the Concepts. Solve and determine whether 8(x - 3) + 4 = 8x - 21 is an identity, a conditional equation, or an inconsistent equation.

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Key Concepts

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

Identity

An identity is an equation that holds true for all values of the variable involved. For example, the equation 2(x + 1) = 2x + 2 is an identity because it simplifies to the same expression regardless of the value of x. Identifying an equation as an identity means that it is universally valid.

Conditional Equation

A conditional equation is an equation that is true only for specific values of the variable. For instance, the equation x + 2 = 5 is conditional because it is only true when x equals 3. Recognizing an equation as conditional indicates that it has a limited set of solutions.

Inconsistent Equation

An inconsistent equation is one that has no solutions at all. For example, the equation x + 1 = x - 1 is inconsistent because there is no value of x that can satisfy it. Identifying an equation as inconsistent means that it cannot be solved for any real number.