Domanda del libro di testo
In Exercises 99–106, solve each equation. 0.7x + 0.4(20) = 0.5(x + 20)
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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 103
Solve each equation in Exercises 83–108 by the method of your choice.
Guida verificata passo dopo passo1
Start with the given quadratic equation: \(2x^2 - 7x = 0\).
Factor out the greatest common factor (GCF) from the terms on the left side. Here, \(x\) is common, so rewrite the equation as \(x(2x - 7) = 0\).
Apply the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero. Set each factor equal to zero: \(x = 0\) and \(2x - 7 = 0\).
Solve each equation separately. The first is already solved: \(x = 0\). For the second, add 7 to both sides to get \(2x = 7\), then divide both sides by 2 to isolate \(x\): \(x = \frac{7}{2}\).
Write the solution set as \(\{0, \frac{7}{2}\}\), which includes all values of \(x\) that satisfy the original equation.
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Factoring Quadratic Equations
Factoring involves rewriting a quadratic equation as a product of simpler expressions set equal to zero. This method is useful when the quadratic can be expressed as a product of binomials or a monomial and a binomial, allowing the use of the zero-product property to find solutions.
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Solving Quadratic Equations by Factoring
Zero-Product Property
The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero. This principle is essential for solving equations after factoring, as it allows setting each factor equal to zero to find the roots of the equation.
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Solving Linear Equations
After factoring, some factors may be linear expressions. Solving linear equations involves isolating the variable on one side to find its value. This step is straightforward and necessary to determine all solutions of the original quadratic equation.
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04:02Solving Linear Equations with Fractions
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