Unlock the power of our free Compound Inequality Calculator to effortlessly solve and visualize complex mathematical statements. Understand the difference between 'AND' (conjunction) and 'OR' (disjunction) inequalities and find their solutions with ease. This tool simplifies expressions like x < 5 AND x > 2 or x ≤ 3 OR x ≥ 7, providing results in both inequality and interval notation.
Formula:
A compound inequality combines two simple inequalities with either 'AND' or 'OR'.
- AND (Conjunction): Both inequalities must be true simultaneously. The solution set is the intersection of their individual solution sets. For example,
x > 2 AND x < 7is true for numbers between 2 and 7. - OR (Disjunction): At least one of the inequalities must be true. The solution set is the union of their individual solution sets. For example,
x ≤ 3 OR x ≥ 8is true for numbers less than or equal to 3, or greater than or equal to 8.
Our calculator takes two simple inequalities (involving 'x' and a constant) and a compound operator ('AND' or 'OR') to determine and display the combined solution in both inequality and interval notation.