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Linear Inequality:
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Interval notation is a mathematical notation used to represent sets of real numbers that satisfy an inequality. It provides a concise way to express solution sets of inequalities using parentheses and brackets.
The calculator solves linear inequalities of the form:
Where:
Explanation: The calculator solves for x and expresses the solution in interval notation, accounting for whether the inequality is strict (>) or inclusive (≥) and whether the coefficient is positive or negative.
Details: Interval notation is widely used in calculus, analysis, and other advanced mathematics to precisely describe domains, ranges, and solution sets. It's more compact than inequality notation and clearly shows whether endpoints are included.
Tips: Enter the coefficients a, b, and c, select the inequality type, and click Calculate. The solution will be shown in standard interval notation.
Q1: What do parentheses and brackets mean in interval notation?
A: Parentheses ( ) indicate the endpoint is not included (strict inequality), while brackets [ ] indicate the endpoint is included (inclusive inequality).
Q2: How does the calculator handle a=0?
A: The calculator requires a non-zero coefficient. If a=0, the inequality becomes a comparison of constants (b > c, etc.).
Q3: What does (-∞, ∞) mean?
A: This represents all real numbers, the solution when the inequality is always true (like 0x + 2 > 1).
Q4: How are solutions represented when a is negative?
A: When multiplying or dividing by a negative number, the inequality sign flips, which affects the interval notation.
Q5: Can this calculator handle quadratic inequalities?
A: No, this calculator is specifically for linear inequalities. Quadratic inequalities require different solution methods.