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In Exercises 1–26, solve and check each linear equation. 3(x - 8) = x
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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TOC.tableOfContents
- Ch. P - Fundamental Concepts of Algebra311
- Ch. 1 - Equations and Inequalities398
- Ch. 2 - Functions and Graphs407
- Ch. 3 - Polynomial and Rational Functions306
- Ch. 4 - Exponential and Logarithmic Functions247
- Ch. 5 - Systems of Equations and Inequalities173
- Ch. 6 - Matrices and Determinants143
- Ch. 7 - Conic Sections124
- Ch. 8 - Sequences, Induction, and Probability251
Capitolo 2, Problema 15
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x-5 = 7
Guida verificata passo dopo passo1
Start with the given equation: \(2x - 5 = 7\).
Add 5 to both sides of the equation to isolate the term with \(x\): \(2x - 5 + 5 = 7 + 5\), which simplifies to \(2x = 12\).
Divide both sides of the equation by 2 to solve for \(x\): \(\frac{2x}{2} = \frac{12}{2}\), which simplifies to \(x = 6\).
Interpret the solution: since \(x = 6\) satisfies the original equation, this is a conditional equation with one solution.
Conclude that the equation is conditional because it is true for a specific value of \(x\) (namely \(x = 6\)), not for all values (identity) or no values (inconsistent).
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Solving Linear Equations
Solving linear equations involves isolating the variable on one side of the equation using inverse operations such as addition, subtraction, multiplication, or division. For example, in 2x - 5 = 7, you add 5 to both sides and then divide by 2 to find x.
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04:02
Solving Linear Equations with Fractions
Types of Equations: Identity, Conditional, and Inconsistent
An identity is true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solution. After solving, you determine which type applies based on the solution set.
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06:00Categorizing Linear Equations
Checking Solutions
After finding a solution, substitute it back into the original equation to verify its validity. This step confirms whether the solution satisfies the equation, helping to classify the equation correctly.
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05:21Restrictions on Rational Equations
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