Inequality Solver - Linear, Quadratic, Polynomial Inequalities | 8gwifi.org

Inequality Solver

Solve linear, quadratic, and polynomial inequalities with interval notation and graphs

Inequality Tools
Linear inequality: ax + b ○ c
where ○ is >, <, ≥, or ≤
Examples:
2x + 3 > 7 → x > 2
-x + 5 ≤ 2 → x ≥ 3
3x ≥ 9 → x ≥ 3
Quadratic inequality: ax² + bx + c ○ 0
Uses factoring, quadratic formula, and sign chart
Cannot be zero
Examples:
x² - 5x + 6 > 0 → x < 2 or x > 3
x² - 4 ≤ 0 → -2 ≤ x ≤ 2
x² + 1 > 0 → All real numbers
Polynomial inequality:
Factor form: (x - r₁)(x - r₂)...(x - rₙ) ○ 0
Enter the roots where the polynomial equals zero
Examples:
(x + 2)(x - 1)(x - 3) > 0 → -2 < x < 1 or x > 3
(x - 1)²(x + 2) ≤ 0 → x ≤ -2 or x = 1
Rational inequality: (x - a)/(x - b) ○ 0
Watch for excluded values (denominator = 0)
This value is EXCLUDED from solution
Examples:
(x - 2)/(x + 1) > 0 → x < -1 or x > 2
1/x ≥ 2 → 0 < x ≤ 0.5
Guide

Solution Methods:

Linear: Solve like equations, flip sign when dividing by negative
Quadratic: Find roots, use sign chart
Polynomial: Test intervals between roots
Rational: Watch for undefined values

Interval Notation:

(a, b) = a < x < b
[a, b] = a ≤ x ≤ b
(-∞, a) = x < a
(a, ∞) = x > a
∪ = union (combines intervals)

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