Ch. 1 - Equations and Inequalities

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

Lial 13th Edition

Ch. 1 - Equations and Inequalities

Problem 8

Chapter 2, Problem 8

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

Verified step by step guidance

Understand the inequality \( |x| \neq 7 \) means the absolute value of \( x \) is not equal to 7. This excludes the points where \( x = 7 \) and \( x = -7 \).

Recall that \( |x| = 7 \) corresponds to the two points \( x = 7 \) and \( x = -7 \) on the number line.

Since the inequality is \( |x| \neq 7 \), the solution set includes all real numbers except \( x = 7 \) and \( x = -7 \).

On the graph, this will be represented by the entire number line with open circles (or holes) at \( x = 7 \) and \( x = -7 \), indicating these points are not included.

Match this description to the graph in Column II that shows all points except \( x = 7 \) and \( x = -7 \) excluded.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Key Concepts

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

Absolute Value

The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. For example, |x| = 7 means x is either 7 or -7, since both are 7 units from zero.

Inequalities Involving Absolute Value

An inequality like |x| ≠ 7 means x cannot be exactly 7 or -7, but can be any other real number. Understanding how to interpret and graph such inequalities is essential for matching them to their solution sets.

Graphing Solution Sets on the Number Line

Graphing solution sets involves representing all values that satisfy an equation or inequality on a number line. For |x| ≠ 7, the graph excludes points at 7 and -7, showing all other points shaded or included.

Recommended video:

02:35

Graphing Lines in Slope-Intercept Form

Related Practice

Textbook Question

Solve each problem. Suppose two acid solutions are mixed. One is 26% acid and the other is 34% acid. Which one of the following concentrations cannot possibly be the concentration of the mixture? A. 24% B. 30% C. 31% D. 33%

views

Textbook Question

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

views

Textbook Question

Decide whether each statement is true or false. The equation 5x=4x is an example of a contradiction.

views

Textbook Question

Use Choices A–D to answer each question. A. 3x² - 17x - 6 = 0 B. (2x + 5)² = 7 C. x² + x = 12 D. (3x - 1)(x - 7) = 0 Which equation is set up for direct use of the zero-factor property? Solve it.

Textbook Question

Decide whether each statement is true or false. If false, correct the right side of the equation. i¹² = 1

Textbook Question

Match each equation in Column I with the correct first step for solving it in Column II. √(x+5) = 7

views