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 31
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
Verified step by step guidance1
Start with the given inequality: \(-9x \geq 36\).
To isolate \(x\), divide both sides of the inequality by \(-9\). Remember, when dividing or multiplying both sides of an inequality by a negative number, the inequality sign must be reversed.
After dividing, the inequality becomes: \(x \leq \frac{36}{-9}\).
Simplify the fraction on the right side to find the numerical value.
Express the solution in interval notation and then graph the solution set on a number line, showing all values of \(x\) that satisfy the inequality.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Solving Linear Inequalities
A linear inequality involves an inequality symbol (>, <, ≥, ≤) with a linear expression. To solve it, isolate the variable on one side by performing inverse operations, similar to solving linear equations, but be mindful of inequality rules.
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Linear Inequalities
Multiplying or Dividing by a Negative Number
When multiplying or dividing both sides of an inequality by a negative number, the direction of the inequality sign must be reversed. This is crucial to maintain the truth of the inequality and avoid incorrect solutions.
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04:22Dividing Complex Numbers
Interval Notation and Graphing Solution Sets
Interval notation expresses solution sets using parentheses or brackets to indicate open or closed intervals. Graphing on a number line visually represents these solutions, showing which values satisfy the inequality and whether endpoints are included.
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05:18Interval Notation
Related Practice
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Solve each radical equation in Exercises 11–30. Check all proposed solutions.
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Textbook Question
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/5 - 1/2 = x/6
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Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 = 2x/3 + 1
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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
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?