Domanda del libro di testo
In Exercises 21–28, divide and express the result in standard form. (2 + 3i)/(2 + i)
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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 27
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/3 = x/2 - 2
Guida verificata passo dopo passo1
Identify the equation: \(\frac{x}{3} = \frac{x}{2} - 2\).
Find the least common denominator (LCD) of the denominators 3 and 2, which is 6.
Multiply every term in the equation by the LCD (6) to eliminate the denominators: \(6 \times \frac{x}{3} = 6 \times \frac{x}{2} - 6 \times 2\).
Simplify each term after multiplication: \(2x = 3x - 12\).
Isolate the variable \(x\) by subtracting \$3x$ from both sides: \(2x - 3x = -12\), then simplify to get $-x = -12$.
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Solving Linear Equations
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and a single variable. Solving such equations involves isolating the variable on one side to find its value. Techniques include combining like terms and performing inverse operations.
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04:02
Solving Linear Equations with Fractions
Clearing Fractions by Multiplying Both Sides
When an equation contains fractions, multiplying both sides by the least common denominator (LCD) eliminates the denominators, simplifying the equation. This step helps avoid dealing with fractions and makes solving the equation more straightforward.
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03:42Linear Inequalities with Fractions & Variables on Both Sides
Checking for Extraneous Solutions
After solving an equation, especially those involving variables in denominators, it is important to check solutions by substituting them back into the original equation. This ensures no solution makes a denominator zero, which would be undefined and thus extraneous.
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05:21Restrictions on Rational Equations
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