Domanda del libro di testo
Solve each equation in Exercises 15–34 by the square root property.
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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 29
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 20 - x/3 = x/2
Guida verificata passo dopo passo1
Identify the equation: \(20 - \frac{x}{3} = \frac{x}{2}\).
To eliminate the denominators, find the least common denominator (LCD) of 3 and 2, which is 6.
Multiply every term in the equation by 6 to clear the fractions: \(6 \times 20 - 6 \times \frac{x}{3} = 6 \times \frac{x}{2}\).
Simplify each term after multiplication: \(120 - 2x = 3x\).
Collect like terms by adding \$2x$ to both sides: \(120 = 3x + 2x\), then combine to get \(120 = 5x\). Finally, solve for $x$ by dividing both sides by 5.
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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. This often requires performing inverse operations like addition, subtraction, multiplication, or division.
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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. This simplifies the equation into a linear form without fractions, making it easier to solve. For example, multiplying both sides by 6 clears denominators 2 and 3.
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03:42Linear Inequalities with Fractions & Variables on Both Sides
Combining Like Terms and Simplifying
After clearing fractions, combine terms with the variable and constants on each side to simplify the equation. This step helps isolate the variable and reduces the equation to a simpler form, facilitating the final solution. Careful arithmetic ensures accuracy in solving.
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03:50Adding & Subtracting Like Radicals
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