Textbook Question
Simplify and write the result in standard form. √-49
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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 30a
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/5 - 1/2 = x/6
Verified step by step guidance1
Step 1: Identify the least common denominator (LCD) of all the denominators in the equation. The denominators are 5, 2, and 6. The LCD is 30.
Step 2: Multiply every term in the equation by the LCD (30) to eliminate the fractions. This gives: 30 * (x/5) - 30 * (1/2) = 30 * (x/6).
Step 3: Simplify each term after multiplying by the LCD. For example, 30 * (x/5) becomes 6x, 30 * (1/2) becomes 15, and 30 * (x/6) becomes 5x. The equation now reads: 6x - 15 = 5x.
Step 4: Isolate the variable x by subtracting 5x from both sides of the equation. This simplifies to: 6x - 5x - 15 = 0, which further simplifies to: x - 15 = 0.
Step 5: Solve for x by adding 15 to both sides of the equation. This gives: x = 15.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Linear Equations
Linear equations are mathematical statements that express the equality of two linear expressions. They typically take the form ax + b = c, where a, b, and c are constants, and x is the variable. Understanding how to manipulate these equations is essential for finding the value of x that satisfies the equation.
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Categorizing Linear Equations
Common Denominator
A common denominator is a shared multiple of the denominators of two or more fractions. When solving equations with fractions, it is often necessary to find a common denominator to eliminate the fractions, making the equation easier to solve. This involves multiplying each term by the least common multiple of the denominators.
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Isolating the Variable
Isolating the variable involves rearranging the equation to get the variable (in this case, x) on one side and the constants on the other. This process typically includes adding, subtracting, multiplying, or dividing both sides of the equation by the same number. Mastering this technique is crucial for solving linear equations effectively.
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Related Practice
Textbook Question
Solve each radical equation in Exercises 11–30. Check all proposed solutions.
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Textbook Question
Solve each equation in Exercises 15–34 by the square root property. (4x - 1)2 = 16
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Textbook Question
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 = 2x/3 + 1
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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. -9x ≥ 36
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Textbook Question
An automobile repair shop charged a customer \$1182, listing \$357 for parts and the remainder for labor. If the cost of labor is \$75 per hour, how many hours of labor did it take to repair the car?
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