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Solve and check each linear equation. 3(x - 1) = 21
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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 5
Solve each equation in Exercises 1 - 14 by factoring.
Guida verificata passo dopo passo1
Start with the quadratic equation: \(6x^2 + 11x - 10 = 0\).
Identify the coefficients: \(a = 6\), \(b = 11\), and \(c = -10\).
Find two numbers that multiply to \(a \times c = 6 \times (-10) = -60\) and add up to \(b = 11\).
Rewrite the middle term \$11x$ as the sum of two terms using the numbers found in the previous step, then group the terms to factor by grouping.
Factor out the greatest common factor (GCF) from each group, then factor the common binomial factor to express the quadratic as a product of two binomials set equal to zero.
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Factoring Quadratic Equations
Factoring quadratic equations involves rewriting the quadratic expression as a product of two binomials. This method is useful for solving equations set to zero by finding values of x that make each factor zero. For example, factoring 6x² + 11x - 10 helps break it down into simpler expressions to solve.
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Solving Quadratic Equations by Factoring
Zero Product Property
The zero product property states that if the product of two factors equals zero, then at least one of the factors must be zero. This principle allows us to set each factor equal to zero and solve for the variable, which is essential after factoring a quadratic equation.
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Solving Linear Equations
After factoring and applying the zero product property, solving linear equations involves isolating the variable to find its value. This step is straightforward and requires basic algebraic manipulation, such as adding, subtracting, multiplying, or dividing both sides of the equation.
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04:02Solving Linear Equations with Fractions
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