Asked by Kirtley Pemberton on Jul 04, 2024
Verified
Write an absolute value inequality that represents the graph. 
A) ∣x∣≤16| x | \leq 16∣x∣≤16 or ∣x∣≥21| x | \geq 21∣x∣≥21
B) ∣x+18.5∣<2.5| x + 18.5 | < 2.5∣x+18.5∣<2.5
C) ∣x−2.5∣<18.5| x - 2.5 | < 18.5∣x−2.5∣<18.5
D) ∣x+2.5∣<18.5| x + 2.5 | < 18.5∣x+2.5∣<18.5
E) ∣x−18.5∣<2.5| x - 18.5 | < 2.5∣x−18.5∣<2.5
Absolute Value Inequality
An inequality that involves the absolute value of a variable expression, requiring consideration of both positive and negative solutions.
Set Notation
A mathematical notation used for describing a collection of distinct objects, typically in the form of {a, b, c,...}.
- Understand the methodology for solving absolute value inequalities.
Verified Answer
AH
abdul hassanJul 05, 2024
Final Answer :
E
Explanation :
The graph appears to have a vertical line of symmetry at x = 18.5, which means that the inequality should involve |x - 18.5|. Additionally, the width of the shading appears to be 2.5 units on either side of the line, which means the inequality should involve < 2.5. The correct inequality is thus |x - 18.5| < 2.5, or choice E.
Learning Objectives
- Understand the methodology for solving absolute value inequalities.