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Ch. 1 - Equations and Inequalities
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 1 - Equations and InequalitiesProblem 5
Chapter 2, Problem 5

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

Verified step by step guidance
1
Identify the inequality given: \(x \geq -6\). This means \(x\) is greater than or equal to \(-6\).
Recall that interval notation uses brackets and parentheses to represent ranges of values. A square bracket \([\) or \(]\) means the endpoint is included (closed interval), while a parenthesis \((\) or \()\) means the endpoint is not included (open interval).
Since the inequality includes \(x \geq -6\), the number \(-6\) is included in the solution set, so we use a square bracket on the left side.
The inequality \(x \geq -6\) means \(x\) can be any number from \(-6\) up to positive infinity. Infinity is never included, so we use a parenthesis on the right side.
Write the interval notation as \([-6, \infty)\) to represent all \(x\) values greater than or equal to \(-6\).

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Key Concepts

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

Inequalities and Their Symbols

Inequalities express the relationship between two values using symbols like ≥, ≤, >, and <. The symbol ≥ means 'greater than or equal to,' indicating all values greater than or exactly equal to a given number. Understanding these symbols is essential to translate inequalities into interval notation.
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Interval Notation

Interval notation is a concise way to represent sets of numbers on the number line. It uses brackets [ ] to include endpoints and parentheses ( ) to exclude them. For example, x ≥ -6 corresponds to the interval [-6, ∞), including -6 and all numbers greater than it.
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Matching Inequalities to Interval Notation

Matching involves identifying the correct interval notation that represents a given inequality. This requires understanding the inequality's direction and whether endpoints are included, then selecting the interval with appropriate brackets and bounds that reflect the inequality accurately.
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