Domanda del libro di testo
Graph each equation in Exercises 13 - 28. Let x = - 3, - 2, - 1, 0, 1, 2, 3
y = x3 - 1
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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
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. 3x - 7 ≥ 13
Guida verificata passo dopo passo1
Start with the given inequality: \(3x - 7 \geq 13\).
Add 7 to both sides to isolate the term with \(x\): \(3x - 7 + 7 \geq 13 + 7\), which simplifies to \(3x \geq 20\).
Divide both sides of the inequality by 3 to solve for \(x\): \(\frac{3x}{3} \geq \frac{20}{3}\), which simplifies to \(x \geq \frac{20}{3}\).
Express the solution set in interval notation: \(\left[ \frac{20}{3}, \infty \right)\), where the square bracket indicates that \(\frac{20}{3}\) is included in the solution.
To graph the solution on a number line, draw a solid dot at \(\frac{20}{3}\) and shade the line extending to the right towards positive infinity.
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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 pay attention to inequality rules, especially when multiplying or dividing by negative numbers.
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06:07
Linear Inequalities
Interval Notation
Interval notation is a way to represent solution sets of inequalities using parentheses and brackets. Parentheses indicate that an endpoint is not included, while brackets mean it is included. For example, [2, ∞) represents all numbers greater than or equal to 2.
Video consigliato:
05:18Interval Notation
Graphing Solution Sets on a Number Line
Graphing solution sets involves marking the range of values that satisfy the inequality on a number line. Use a solid dot for included endpoints (≥ or ≤) and an open circle for excluded endpoints (> or <). Shade the region representing all solutions to visually display the set.
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02:35Graphing Lines in Slope-Intercept Form
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