Textbook Question
Simplify and write the result in standard form. √-108
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 33
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. 8x - 11 ≤ 3x - 13
Verified step by step guidance1
Start by isolating the variable term on one side of the inequality. Subtract from both sides: .
Combine like terms on the left-hand side: .
Next, isolate the term with the variable by adding to both sides: .
Simplify the right-hand side: .
Finally, divide both sides of the inequality by to solve for : . Express the solution in interval notation and graph it on a number line.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Linear Inequalities
Linear inequalities are mathematical expressions that involve a linear function and an inequality sign (such as ≤, ≥, <, or >). They represent a range of values rather than a single solution. Understanding how to manipulate these inequalities is crucial for solving them, as it involves similar techniques to solving linear equations, but with special attention to the direction of the inequality when multiplying or dividing by negative numbers.
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Linear Inequalities
Interval Notation
Interval notation is a mathematical notation used to represent a range of values on the real number line. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). For example, the interval (2, 5] includes all numbers greater than 2 and up to 5, including 5. This notation is essential for expressing the solution sets of inequalities succinctly.
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05:18Interval Notation
Graphing on a Number Line
Graphing solution sets on a number line visually represents the range of values that satisfy an inequality. This involves marking points and using open or closed circles to indicate whether endpoints are included or excluded. Understanding how to accurately depict these solutions helps in interpreting the results of inequalities and provides a clear visual reference for the solution set.
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02:35Graphing Lines in Slope-Intercept Form
Related Practice
Textbook Question
Solve each equation in Exercises 15–34 by the square root property. (8x - 3)2 = 5
Textbook Question
For an international telephone call, a telephone company charges \$0.43 for the first minute, \$0.32 for each additional minute, and a \$2.10 service charge. If the cost of a call is \$5.73, how long did the person talk?
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Textbook Question
A repair bill on a sailboat came to \$2356, including \$826 for parts and the remainder for labor. If the cost of labor is \$90 per hour, how many hours of labor did it take to repair the sailboat?
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Textbook Question
In Exercises 29–36, simplify and write the result in standard form. √(32 - 4 × 2 × 5)
Textbook Question
Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)3/2 = 27