Examples on Absolute Value Inequalities
Example 1: Solve for inequality |x+24|>-5 using the formula-based approach.
Solution:
Given Inequality
|x + a| > b
- -∞ < x + a < -b
- b < x + a < +∞
Solving both of them individually
Case 1:
-∞ < x < -a – b
Case 2:
b – a < x < ∞
x ⋿ (-∞,-a-b) ⋃ (b-a, ∞)
Example 2: Solve this less than equal to absolute inequality |y + 5| <= 3y
Solution:
Given Inequality
- |y + 5| <= 3y
Case 1:
y + 5 <= 3y
5 <= 2y
5/2 <= y
y ϵ [5/2, ∞)…(i)
Case 2:
-3y <= y + 5
-4y <= 5
y >= -1.25
y ϵ (-∞, -5/4]…(ii)
From eq. (i) and eq. (ii)
y ϵ [5/2, -5/4]
Absolute Value Inequalities
Inequalities that involve algebraic expressions with absolute value symbols and inequality symbols are called Absolute Value Inequality. In this article, we will discuss inequalities and absolute value inequalities and others in detail.
Table of Content
- What is Inequalities?
- What is Absolute Value Inequalities?
- Solving Absolute Value Inequalities
- Types of Absolute Value Inequalities
- Intersection and Union in Absolute Value Inequalities
- Examples on Absolute Value Inequalities
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