Ch. 1 - Equations and Inequalities

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 1 - Equations and Inequalities

Problem 6

Chapter 2, Problem 6

Match the inequality in each exercise in Column I with its equivalent interval notation in Column II. 6≤x

Verified step by step guidance

Identify the inequality given: \(6 \leq x\). This means that \(x\) is greater than or equal to 6.

Recall that interval notation expresses the set of all values that satisfy the inequality using brackets and parentheses.

Since \(x\) is greater than or equal to 6, the interval starts at 6 and extends to positive infinity.

Use a square bracket \([\( to include 6 because of the 'greater than or equal to' (\(\leq\)) symbol, and use a parenthesis \))\) for infinity since infinity is not a number and cannot be included.

Write the interval notation as \([6, \infty)\) to represent all \(x\) such that \(x \geq 6\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Inequalities

Inequalities express a relationship where one quantity is greater than, less than, or equal to another. In this case, 6 ≤ x means x is any number greater than or equal to 6. Understanding how to interpret and manipulate inequalities is essential for solving and matching them to interval notation.

Interval Notation

Interval notation is a concise way to represent sets of numbers between two endpoints. It uses brackets [ ] to include endpoints and parentheses ( ) to exclude them. For example, 6 ≤ x corresponds to the interval [6, ∞), indicating all numbers from 6 to infinity, including 6.

Set Representation of Solutions

Inequalities and interval notation both describe solution sets for variables. Recognizing how to translate between these forms helps in understanding the range of possible values. This concept involves identifying whether endpoints are included and whether the set extends infinitely or is bounded.

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