Textbook Question
In Exercises 21–28, divide and express the result in standard form. 5i/(2 - i)
2
views
Ch. 1 - Equations and Inequalities
Blitzer8th EditionCollege AlgebraISBN: 9780136970514
Not the one you use?Change textbookSelect a different textbook
Table of contents
- 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
Chapter 2, Problem 25
In Exercises 15–26, use graphs to find each set. [3, ∞) ⋃ (6, ∞)
Verified step by step guidance1
Understand the problem: You are asked to find the union of two intervals, \([3, \infty)\) and \((6, \infty)\), using graphs. The union means all values that belong to either interval or both.
Graph the first interval \([3, \infty)\) on a number line. This includes all numbers starting at 3 (including 3) and extending to positive infinity. Represent this with a solid dot at 3 and a ray extending to the right.
Graph the second interval \((6, \infty)\) on the same number line. This includes all numbers greater than 6 but not including 6. Represent this with an open dot at 6 and a ray extending to the right.
Identify the union of these two intervals on the graph. Since \([3, \infty)\) already includes all numbers from 3 onwards, and \((6, \infty)\) is a subset of that starting from 6, the union will cover all numbers starting at 3 and going to infinity.
Write the union interval notation based on the graph: it will be \([3, \infty)\) because this interval already contains all elements of both sets.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Interval Notation
Interval notation is a way to represent sets of real numbers using brackets and parentheses. Square brackets [ ] include the endpoint, while parentheses ( ) exclude it. For example, [3, ∞) includes all numbers from 3 to infinity, including 3.
Recommended video:
05:18
Interval Notation
Union of Sets
The union of two sets combines all elements from both sets without duplication. In interval notation, the union symbol (∪) merges intervals, so [3, ∞) ∪ (6, ∞) includes all numbers from 3 onwards, considering overlaps.
Recommended video:
5:10Finding the Domain and Range of a Graph
Graphing Intervals on the Number Line
Graphing intervals involves shading regions on a number line to represent sets of numbers. Closed dots indicate included endpoints, open dots indicate excluded endpoints, and shading shows all numbers within the interval, helping visualize unions and intersections.
Recommended video:
Guided course
02:35Graphing Lines in Slope-Intercept Form
Related Practice
Textbook Question
Solve each equation in Exercises 15–34 by the square root property.
Textbook Question
Solve and check each linear equation. 25 - [2 + 5y - 3(y + 2)] = - 3(2y - 5) - [5(y - 1) - 3y + 3]
2
views
Textbook Question
Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x/3 = 6 - x/4
5
views
Textbook Question
Divide and express the result in standard form. 8i/(4 - 3i)
Textbook Question
A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?