교과서 질문
Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 3) = 1/4
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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
2장, 문제 105
In Exercises 104–106, express each interval in set-builder notation and graph the interval on a number line. (-2, ∞)
검증된 단계별 안내1
Understand the given interval: The interval (-2, ∞) represents all real numbers greater than -2 but not including -2 itself. The parentheses indicate that -2 is not part of the interval, and ∞ means the interval extends indefinitely in the positive direction.
Convert the interval to set-builder notation: In set-builder notation, we describe the set of numbers using a condition. For this interval, the condition is that x is greater than -2. This can be written as {x | x > -2}, where the vertical bar '|' means 'such that.'
Prepare to graph the interval on a number line: To graph the interval (-2, ∞), start by marking the point -2 on the number line. Since -2 is not included in the interval, use an open circle at -2 to indicate this.
Draw the graph: From the open circle at -2, draw a line extending to the right indefinitely to represent all numbers greater than -2. Add an arrow at the end of the line to show that the interval continues infinitely.
Review the solution: The interval (-2, ∞) is expressed in set-builder notation as {x | x > -2}, and the graph includes an open circle at -2 with a line extending to the right indefinitely.
비슷한 문제에 대한 검증된 영상 답변:
이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
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주요 개념
질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.
Set-Builder Notation
Set-builder notation is a mathematical shorthand used to describe a set by specifying a property that its members must satisfy. For example, the interval (-2, ∞) can be expressed in set-builder notation as {x | x > -2}, meaning 'the set of all x such that x is greater than -2'. This notation is particularly useful for defining intervals and sets in a concise manner.
추천 영상:
05:18
Interval Notation
Intervals
An interval is a range of numbers between two endpoints. Intervals can be open, closed, or half-open, depending on whether the endpoints are included. The interval (-2, ∞) is an open interval starting at -2 and extending indefinitely to the right, meaning -2 is not included in the set, but all numbers greater than -2 are.
추천 영상:
05:18Interval Notation
Graphing on a Number Line
Graphing an interval on a number line involves visually representing the range of values included in the interval. For the interval (-2, ∞), you would place an open circle at -2 to indicate that it is not included, and then shade the line to the right to show that all numbers greater than -2 are part of the interval. This visual representation helps in understanding the extent of the interval.
추천 영상:
02:35Graphing Lines in Slope-Intercept Form
관련 실천
교과서 질문
Use the table to solve each inequality. - 3 < 2x - 5 ≤ 3
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교과서 질문
Solve each equation. 4x + 13 - {2x - [4(x - 3) - 5]} = 2(x - 6)
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교과서 질문
Use the graph of y = |4 - x| to solve each inequality.
|4 - x| ≥ 5
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교과서 질문
Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 2) = 1/3
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교과서 질문
In Exercises 101–106, solve each equation.
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