Inequality

A mathematical representation of an inequality, with the initial equation "3x + 2 ≥ 8" simplified step by step to "x ≥ 2," accompanied by a number line graph illustrating the solution set starting at 2 and extending to infinity.
Solving the inequality "3x + 2 ≥ 8" narrows down the values of x to all numbers greater than or equal to 2, depicted on a number line as the set [2, ∞).

Table of Contents

What is an Inequality?

Inequality is a mathematical statement that expresses a relationship between two expressions, typically denoted by one of the inequality symbols: < (less than), > (greater than), \le (less than or equal to), \ge (greater than or equal to), or \ne (not equal to).

An inequality indicates that one expression has a certain relationship with another, such as being smaller, greater, or not equal.

Notation

  • a<b means a is less than b.
  • a>b means a is greater than b.
  • a\le b means a is less than or equal to b.
  • a\ge b means a is greater than or equal to b.
  • a\ne b means ais not equal to b.

Examples of Inequalities

  1. Strict Inequality: x<5, This inequality states that x is less than 5, but not equal to 5.

  2. Non-strict Inequality: y\ge \text{-}2, This inequality states that y is greater than or equal to –2.

  3. Compound Inequality: \text{-}3<z\le 1, This compound inequality combines two inequalities and indicates that z is greater than –3 and less than or equal to 1.

  4. Absolute Value Inequality: |x-4|< 3, This inequality involves the absolute value and states that the distance between x and 4 is less than 3.

  5. Inequality with Variables: 2y+7\ge 13, This inequality involves a variable y and states that 2y+7 is greater than or equal to 13.

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Base (Algebra)

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Factors

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