Use <, >, <=, >= for inequality symbols
Adding/Subtracting
Inequality direction stays the same
Multiplying/Dividing by Positive
Inequality direction stays the same
Multiplying/Dividing by Negative
Inequality direction FLIPS
Less than
Greater than
Less than or equal
Greater than or equal
Single:
2x - 5 > 3x + 1Compound:
1 < 2x + 3 <= 7Absolute Value:
|x - 3| < 5Inequalities are mathematical expressions that compare two values using symbols like less than (<), greater than (>), less than or equal to (≤), or greater than or equal to (≥). Unlike equations that have specific solutions, inequalities often have ranges of values that satisfy them. They are fundamental in algebra and have applications in optimization, economics, physics, and everyday decision-making where constraints need to be expressed mathematically.
Linear Inequalities
Inequalities involving a single variable raised to the first power, like 2x + 5 > 11. The solution is typically a range of values on one side of a boundary point.
Compound Inequalities
Two inequalities joined by AND or OR. AND inequalities (like 1 < x < 5) require both conditions to be true, while OR inequalities satisfy at least one condition.
Absolute Value Inequalities
Inequalities containing absolute value expressions like |x - 3| < 5. These are solved by considering the distance from a point, resulting in compound inequalities.
Disclaimer
This inequality solver applies standard algebraic rules. Results depend on correct input formatting and mathematical assumptions. Always verify solutions for critical applications.