Textbook Question
Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8.
, for t
Ch. 1 - Equations and Inequalities
Lial13th EditionCollege AlgebraISBN: 9780136881063
Not the one you use?Change textbookSelect a different textbook
Table of contents
Chapter 2, Problem 74
Write each statement using an absolute value equation or inequality.
q is no more than 8 units from 22.
Verified step by step guidance1
Identify the key phrase "no more than 8 units from 22," which means the distance between q and 22 is at most 8.
Recall that the absolute value expression \(\left| q - a \right|\) represents the distance between q and a on the number line.
Translate the phrase into the inequality \(\left| q - 22 \right| \leq 8\), where the absolute value measures the distance from 22.
Understand that the inequality \(\left| q - 22 \right| \leq 8\) means q is within 8 units either less than or greater than 22.
This absolute value inequality correctly represents the statement "q is no more than 8 units from 22."
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
1mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Absolute Value Definition
The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. For any number x, |x| denotes this distance, so |x| ≥ 0. This concept helps express distances regardless of direction.
Recommended video:
08:07
Vertex Form
Translating Distance Statements into Absolute Value
When a variable is described as being within a certain distance from a number, it can be expressed as an absolute value inequality. For example, 'q is no more than 8 units from 22' translates to |q - 22| ≤ 8, representing all values q within 8 units of 22.
Recommended video:
7:30Logarithms Introduction
Formulating Absolute Value Inequalities
Absolute value inequalities like |x - a| ≤ b describe all values x within a distance b from a fixed point a. This inequality can be rewritten as a compound inequality a - b ≤ x ≤ a + b, which helps in solving or graphing the solution set.
Recommended video:
06:07Linear Inequalities
Related Practice
Textbook Question
Solve each equation. √4x-2 = √3x+1
3
views
Textbook Question
Solve each rational inequality. Give the solution set in interval notation. 3/(2x-1)>-4/x
Textbook Question
Solve each equation. ∜(x2+2x)= ∜3
2
views
Textbook Question
Solve each equation. x3/2 = 125
Textbook Question
Solve each rational inequality. Give the solution set in interval notation. 4/(3+x)≤3/(3+x)