Textbook Question
In Exercises 59–94, solve each absolute value inequality. |3 - (2/3)x| > 5
Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- 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
Chapter 2, Problem 76a
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 7 = 2x + 7
Verified step by step guidance1
Start by isolating the variable term on one side of the equation. Subtract 2x from both sides of the equation: .
Simplify the equation by combining like terms: , which simplifies to .
Next, isolate the term with the variable by subtracting 7 from both sides: .
Simplify the equation further: .
Finally, solve for by dividing both sides of the equation by 3: . After solving, determine whether the equation is an identity, a conditional equation, or an inconsistent equation based on the solution.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Types of Equations
In algebra, equations can be classified into three main types: identities, conditional equations, and inconsistent equations. An identity is true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solutions. Understanding these classifications helps in determining the nature of the solution set for any given equation.
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Types of Slope
Solving Linear Equations
Solving linear equations involves isolating the variable to find its value. This typically includes combining like terms, using inverse operations, and simplifying both sides of the equation. For the equation 5x + 7 = 2x + 7, one would rearrange the terms to isolate x, which is essential for determining the type of equation it represents.
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Checking Solutions
After solving an equation, it is crucial to check the solution by substituting it back into the original equation. This verification process confirms whether the solution is valid and helps identify the type of equation. For instance, if the left-hand side equals the right-hand side after substitution, it indicates whether the equation is an identity or a conditional equation.
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Related Practice
Textbook Question
Exercises 73–75 will help you prepare for the material covered in the next section. Rationalize the denominator: (7 + 4√2)/(2 - 5√2).
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Textbook Question
In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation.
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Textbook Question
In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| + 3 = 3
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Textbook Question
Solve each equation by the method of your choice.
Textbook Question
Solve each equation by the method of your choice.