Domanda del libro di testo
Without solving the given quadratic equation, determine the number and type of solutions.
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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 72a
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4x + 7 = 7(x + 1) - 3x
Guida verificata passo dopo passo1
Start by simplifying both sides of the equation. On the right-hand side, distribute the 7 across the terms inside the parentheses: 7(x + 1) becomes 7x + 7. The equation now looks like 4x + 7 = 7x + 7 - 3x.
Combine like terms on the right-hand side. Combine 7x and -3x to get 4x. The equation now simplifies to 4x + 7 = 4x + 7.
Next, subtract 4x from both sides of the equation to isolate the constants. This simplifies the equation to 7 = 7.
Analyze the resulting equation. Since 7 = 7 is always true, the original equation is true for all values of x.
Conclude that the equation is an identity because it holds true for all values of x.
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Solving Linear Equations
Solving linear equations involves finding the value of the variable that makes the equation true. This typically requires isolating the variable on one side of the equation through operations such as addition, subtraction, multiplication, and division. In the given equation, simplifying both sides will help identify the solution.
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Solving Linear Equations with Fractions
Types of Equations
Equations can be classified into three types: identities, conditional equations, and inconsistent equations. An identity holds true for all values of the variable, a conditional equation is true for specific values, and an inconsistent equation has no solution. Understanding these classifications is essential for determining the nature of the solution after solving the equation.
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Simplifying Expressions
Simplifying expressions involves combining like terms and applying the distributive property to make equations easier to solve. In the context of the given equation, distributing the 7 on the right side and combining terms will lead to a clearer path to finding the solution. This step is crucial for accurately determining the type of equation.
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05:07Simplifying Algebraic Expressions
Pratica correlata
Domanda del libro di testo
In Exercises 59–94, solve each absolute value inequality. |3x - 8| > 7
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Domanda del libro di testo
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 9 = 9(x + 1) - 4x
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In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x + 1| + 5 = 3
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Exercises 73–75 will help you prepare for the material covered in the next section. Multiply: (7 - 3x)(- 2 - 5x)
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Solve each equation in Exercises 65–74 using the quadratic formula.
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