Domanda del libro di testo
Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 5 + (x - 2)/3 = (x + 3)/8
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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 39
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. 1 - (x + 3) ≥ 4 - 2x
Guida verificata passo dopo passo1
Start by rewriting the inequality clearly: \(1 - (x + 3) \geq 4 - 2x\).
Distribute the negative sign across the parentheses on the left side: \(1 - x - 3 \geq 4 - 2x\).
Combine like terms on the left side: \((1 - 3) - x \geq 4 - 2x\) which simplifies to \(-2 - x \geq 4 - 2x\).
Add \$2x$ to both sides to get all $x$ terms on one side: \(-2 - x + 2x \geq 4 - 2x + 2x\), simplifying to \(-2 + x \geq 4\).
Add 2 to both sides to isolate the \(x\) term: \(-2 + x + 2 \geq 4 + 2\), which simplifies to \(x \geq 6\).
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Solving Linear Inequalities
Solving linear inequalities involves isolating the variable on one side to find the range of values that satisfy the inequality. Similar to equations, you perform operations like addition, subtraction, multiplication, or division, but must reverse the inequality sign when multiplying or dividing by a negative number.
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06:07
Linear Inequalities
Interval Notation
Interval notation is a concise way to represent sets of numbers that satisfy inequalities. It uses parentheses () for values not included and brackets [] for values included, indicating the start and end points of the solution set on the number line.
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05:18Interval Notation
Graphing Solution Sets on a Number Line
Graphing solution sets involves marking the values that satisfy the inequality on a number line. Use open circles for values not included and closed circles for included values, shading the region that represents all possible solutions.
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02:35Graphing Lines in Slope-Intercept Form
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