Textbook Question
In Exercises 29–36, simplify and write the result in standard form. √(12 - 4 × 0.5 × 5)
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Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
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Table of contents
- 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
Chapter 2, Problem 35
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. (x + 3)/6 = 3/8 + (x - 5)/4
Verified step by step guidance1
Identify the given equation: \(\frac{(x + 3)}{6} = \frac{3}{8} + \frac{(x - 5)}{4}\).
Find the least common denominator (LCD) of all denominators (6, 8, and 4). The LCD is 24.
Multiply every term on both sides of the equation by 24 to eliminate the denominators: \(24 \times \frac{(x + 3)}{6} = 24 \times \frac{3}{8} + 24 \times \frac{(x - 5)}{4}\).
Simplify each term after multiplication: \(4(x + 3) = 3 \times 3 + 6(x - 5)\).
Distribute and combine like terms to form a linear equation without fractions, then solve for \(x\) by isolating the variable on one side.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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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Solving Linear Equations with Fractions
Clearing Fractions by Finding a Common Denominator
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 directly and makes solving the equation more straightforward.
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Properties of Equality
Properties of equality, such as the addition, subtraction, multiplication, and division properties, allow you to perform the same operation on both sides of an equation without changing its solution. These properties are essential for manipulating and simplifying equations to isolate the variable.
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Related Practice
Textbook Question
In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? A = (1/2)bh for b
Textbook Question
In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.
Textbook Question
Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)2/3 = 16
Textbook Question
In all exercises, other than exercises with no solution, use interval notation to express solution sets and graph each solution set on a number line. In Exercises 27–50, solve each linear inequality. 4(x + 1) + 2 ≥ 3x + 6
Textbook Question
Solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? D = RT for R