Example 1
\(2x + 3 > 7 \rightarrow x > 2\)
Ungleichungslöser
Lösen Sie lineare Ungleichungen mit einer Variablen und visualisieren Sie Lösungen auf der Zahlengeraden
Ergebnisse
Geben Sie Werte ein und klicken Sie auf Berechnen, um das Ergebnis zu sehen.
Theory & Formula
A linear inequality is similar to a linear equation, but instead of equality, it uses inequality symbols (<, >, ≤, ≥).
Key rules for solving inequalities:
- Addition/Subtraction: Adding or subtracting the same value on both sides preserves the inequality
- Multiplication/Division (positive): Multiplying or dividing by a positive number preserves the inequality
- Multiplication/Division (negative): Multiplying or dividing by a negative number reverses the inequality
- Solution set: An inequality typically has infinitely many solutions, represented on a number line or in interval notation
\(ax + b < c \rightarrow x < \frac{c - b}{a}\) (if \(a > 0\))
Worked Examples
Example 2
\(-3x + 5 \leq 14 \rightarrow x \geq -3\)
Example 3
\(5x - 2 < 13 \rightarrow x < 3\)
Interval Notation
\(x \geq 2\) is written as \([2, \infty)\)