Inequality to Interval Notation Calculator

Interval notation expresses the set of all real numbers that satisfy a given inequality using parentheses and brackets. Parentheses like ( ) indicate strict inequalities where endpoints are excluded (less than or greater than), while square brackets [ ] denote inclusive endpoints (less than or equal to, or greater than or equal to). Compound inequalities combining multiple conditions use union symbols (U) to link separate ranges, translating algebraic constraints into precise geometric boundaries on the number line.

Let us convert the compound inequality -3 < x ≤ 5 into interval notation. First, identify the lower and upper bounds of the inequality, which are -3 and 5 respectively. Next, examine the inequality operators: the strict inequality operator (<) at the lower bound means we use a parenthesis, while the inclusive operator (≤) at the upper bound requires a square bracket. Combining these components yields the final interval notation: (-3, 5].

Always list interval values from left to right, starting with the smaller number and ending with the larger number. Never use a square bracket next to infinity or negative infinity symbols, as infinity represents an ongoing concept rather than a fixed number point. Double-check your boundary operators before finalizing brackets versus parentheses to prevent common graphing mistakes.