Domanda del libro di testo
Solve each equation in Exercises 65–74 using the quadratic formula. x2 - 6x + 10 = 0
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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 74
In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4(x + 5) = 21 + 4x
Guida verificata passo dopo passo1
Start by expanding the left side of the equation using the distributive property: \(4(x + 5) = 4 \times x + 4 \times 5\).
Rewrite the equation after distribution: \(4x + 20 = 21 + 4x\).
Next, subtract \$4x$ from both sides to begin isolating the constants: \(4x + 20 - 4x = 21 + 4x - 4x\).
Simplify both sides: \(20 = 21\).
Analyze the resulting statement: since \(20 = 21\) is false, conclude whether the equation is an identity, conditional, or inconsistent based on this contradiction.
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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, and division. The goal is to find the value of the variable that makes the equation true.
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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. Identifying the type depends on the solution set after simplifying the equation.
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Distributive Property
The distributive property allows you to multiply a single term by each term inside parentheses, e.g., a(b + c) = ab + ac. This property is essential for simplifying expressions before solving equations.
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04:15Multiply Polynomials Using the Distributive Property
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