Inequality Solver - Solve Linear, Quadratic & Absolute Value Inequalities
Inequality Type
ax + b > 0
Enter coefficients and select inequality sign. Solution will be shown on number line.
Solution
Enter coefficients and click Solve
Understanding Inequalities
What is an Inequality?
An inequality expresses that one value is less than, greater than, or not equal to another. Unlike equations which have specific solutions, inequalities often have a range of solutions.
<
Less than
≤
Less or equal
>
Greater than
≥
Greater or equal
Linear Inequalities
ax + b > 0
Solve like equations, but flip the sign when dividing by negative numbers.
Quadratic Inequalities
ax² + bx + c < 0
Find roots and test intervals to determine solution regions.
Absolute Value
|ax + b| < c
Split into two cases: positive and negative expressions.
Interval Notation Guide
(a, b)Open interval: a < x < b (endpoints excluded)[a, b]Closed interval: a ≤ x ≤ b (endpoints included)(a, ∞)x > a (extends to positive infinity)(-∞, b)x < b (extends to negative infinity)(a, b) ∪ (c, d)Union: x in (a,b) OR x in (c,d)Key Rules
- • Adding/subtracting: Same number on both sides, sign stays same
- • Multiply/divide by positive: Sign stays same
- • Multiply/divide by negative: Flip the inequality sign!
- • Number line: Solid dot = included, hollow dot = excluded
- • Checking: Pick test points from each region to verify