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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 4
Chapter 2, Problem 4

Match the inequality in each exercise in Column I with its equivalent interval notation in Column II. x2≥0
Matching exercise with inequalities in Column I and interval notations in Column II, including number line graphs for some intervals.

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1
Recognize that the inequality given is \(x^2 \geq 0\). This means we are looking for all values of \(x\) such that the square of \(x\) is greater than or equal to zero.
Recall that the square of any real number is always non-negative, so \(x^2 \geq 0\) is true for every real number \(x\).
Therefore, the solution set includes all real numbers, which in interval notation is expressed as \((-\infty, \infty)\).
Match the inequality \(x^2 \geq 0\) from Column I with the interval notation \((-\infty, \infty)\) from Column II.
Confirm that this interval notation correctly represents the solution set of the inequality, meaning all real numbers satisfy the inequality.

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Key Concepts

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

Inequalities and Their Solutions

An inequality compares two expressions using symbols like ≥, ≤, >, or <. Solving an inequality involves finding all values of the variable that make the inequality true. For example, x² ≥ 0 means finding all x such that the square of x is nonnegative.
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Properties of Squares of Real Numbers

The square of any real number x, denoted x², is always greater than or equal to zero. This property implies that x² ≥ 0 holds for all real numbers x, which is important when translating inequalities involving squares into interval notation.
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Imaginary Roots with the Square Root Property

Interval Notation

Interval notation is a way to represent sets of numbers between two endpoints. It uses brackets [ ] for inclusive boundaries and parentheses ( ) for exclusive boundaries. For example, the solution to x² ≥ 0 is all real numbers, represented as (-∞, ∞) in interval notation.
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Related Practice
Textbook Question

Match the equation in Column I with its solution(s) in Column II. x2 - 5 = 0

Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | < 7

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Textbook Question

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

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Textbook Question

Match each equation or inequality in Column I with the graph of its solution set in Column II. | x | > 7

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Textbook Question

Solve each equation. A= 24f / B(p+1), for f (approximate annual interest rate)

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Textbook Question

Answer each question. Sides of a Right TriangleTo solve for the lengths of the right triangle sides, which equation is correct?

A. x^2=(2x-2)^2+(x+4)^2 B. x^2+(x+4)^2=(2x-2)^2 C. x^2=(2x-2)^2-(x+4)^2 D. x^2+(2x-2)^2=(x+4)^2