Domanda del libro di testo
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. (3x+1)/3 - 13/2 = (1-x)/4
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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 27
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. 5x + 11 < 26
Guida verificata passo dopo passo1
Start with the given inequality: \(5x + 11 < 26\).
Isolate the term with the variable by subtracting 11 from both sides: \(5x + 11 - 11 < 26 - 11\), which simplifies to \(5x < 15\).
Next, solve for \(x\) by dividing both sides of the inequality by 5: \(\frac{5x}{5} < \frac{15}{5}\), which simplifies to \(x < 3\).
Express the solution set in interval notation. Since \(x\) is less than 3, the solution is all real numbers less than 3, written as \((-\infty, 3)\).
To graph the solution on a number line, draw a number line, place an open circle at 3 (because 3 is not included), and shade all points to the left of 3.
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Solving Linear Inequalities
A linear inequality involves an inequality symbol (<, >, ≤, ≥) with a linear expression. To solve it, isolate the variable by performing inverse operations, similar to solving linear equations, but remember to reverse the inequality sign when multiplying or dividing by a negative number.
Video consigliato:
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, (a, b) means all numbers between a and b, excluding a and b.
Video consigliato:
05:18Interval Notation
Graphing Solution Sets on a Number Line
Graphing solution sets involves shading the region on a number line that satisfies the inequality. Open circles represent excluded endpoints, and closed circles represent included endpoints. This visual helps understand the range of possible values for the variable.
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02:35Graphing Lines in Slope-Intercept Form
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