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
2:09 minutes
Problem 33c
Textbook Question
Textbook QuestionDetermine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution set. 2(x-8) = 3x-16
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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) = 2x is an identity because it is valid for any value of x. In solving equations, if both sides simplify to the same expression regardless of the variable's value, the equation is classified as an identity.
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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. When solving such equations, the solution set consists of the values that satisfy the equation.
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Contradiction
A contradiction is an equation that has no solution because it is never true for any value of the variable. An example is the equation x + 1 = x, which simplifies to 1 = 0, a false statement. In this case, the solution set is empty, indicating that there are no values that can satisfy the equation.
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