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Solve and check each linear equation. 4x + 9 = 33
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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 1
In Exercises 1–14, express each interval in set-builder notation and graph the interval on a number line. (1, 6]
Guida verificata passo dopo passo1
Identify the interval type: (1, 6] means the interval includes all numbers greater than 1 but less than or equal to 6.
Write the inequality that represents this interval: \(1 < x \leq 6\).
Express the interval in set-builder notation using the inequality: \(\{ x \mid 1 < x \leq 6 \}\).
To graph the interval on a number line, draw a number line and mark the points 1 and 6.
Use an open circle at 1 to show that 1 is not included, and a closed circle at 6 to show that 6 is included; then shade the region between 1 and 6.
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Interval Notation
Interval notation is a way to represent a set of numbers between two endpoints. Parentheses () indicate that an endpoint is not included (open), while brackets [] mean the endpoint is included (closed). For example, (1, 6] includes all numbers greater than 1 and up to and including 6.
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05:18
Interval Notation
Set-Builder Notation
Set-builder notation describes a set by specifying a property that its members satisfy. It typically uses a variable and a condition, such as {x | 1 < x ≤ 6}, meaning the set of all x such that x is greater than 1 and less than or equal to 6.
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05:18Interval Notation
Graphing Intervals on a Number Line
Graphing intervals involves marking the endpoints on a number line and indicating whether they are included or excluded. Use an open circle for excluded endpoints and a closed circle for included endpoints, then shade the region between to represent all numbers in the interval.
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02:35Graphing Lines in Slope-Intercept Form
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