Representation Math Example 2

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Example 2

medium
The inequality ∣x−3∣<2|x - 3| < 2 can be represented as an absolute value inequality, a compound inequality, and an interval. Convert between all three.

Solution

  1. 1
    Absolute value form: ∣x−3∣<2|x-3| < 2.
  2. 2
    Compound inequality: −2<x−3<2-2 < x - 3 < 2, which gives 1<x<51 < x < 5.
  3. 3
    Interval notation: x∈(1,5)x \in (1, 5).
  4. 4
    Number line: a segment from 1 to 5, with open circles at the endpoints.

Answer

∣x−3∣<2  ⟺  1<x<5  ⟺  x∈(1,5)|x-3|<2 \iff 1 < x < 5 \iff x \in (1,5)
Multiple representations of the same condition allow flexibility in solving and reasoning. Absolute value, compound inequality, and interval notation each highlight different features.

About Representation

A mathematical representation is any format — diagram, equation, table, graph, or symbolic expression — used to encode and communicate a mathematical idea or relationship between quantities.

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More Representation Examples

Example 1 easy

Represent the set [formula] with [formula] and [formula] using three different representations: (1)

Example 3 easy

Write the solution set of [formula] in (a) roster notation, (b) set-builder notation.

Example 4 medium

A function [formula] triples its input. Represent [formula] as (a) a formula, (b) a table for inputs

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