Math Problem Statement

Solve questions

Solve the inequalities |x+1| < |x-2| and |x| > |2x-3|.

Solution

Let us solve each of the inequalities involving absolute values:

Problem e) ∣x+1∣<∣x−2∣|x+1| < |x-2|

To solve ∣x+1∣<∣x−2∣|x+1| < |x-2|, consider two cases:

  1. When x+1x+1 and x−2x-2 are both positive or both negative:
    • For this scenario, the inequality reduces to x+1<x−2x+1 < x-2, but in-hand___ -> _[].

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Math Problem Analysis

Mathematical Concepts

Absolute Values
Inequalities
Case Analysis in Algebra

Formulas

Definition of Absolute Value: |a| = a if a ≥ 0, -a if a < 0

Theorems

Properties of Inequalities with Absolute Values

Suitable Grade Level

Grades 10-12

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