Compound Inequality Calculator

Solve compound inequalities (AND / OR), graph solutions on a number line, and get step-by-step explanations.

Inequality Type

Solution Format

Left Expression

Operator

Right Value

First Inequality

Second Inequality

Left Bound

Middle Expression

Right Bound

Expression inside | |

Operator & Value

Solution

-

Number Line Graph

Step-by-Step Solution

Enter an inequality and click "Solve Inequality" to see the step-by-step solution.

Inequality Rules

Adding/subtracting same number to both sides
Multiplying/dividing by positive number preserves inequality
Multiplying/dividing by negative number flips inequality sign
Compound AND: both conditions must be true
Compound OR: at least one condition must be true

Interval Notation Guide

(a, b): a < x < b (open circle)
[a, b]: a ≤ x ≤ b (closed circle)
(-∞, a): x < a
(a, ∞): x > a
∪: Union (OR)

Compound Inequality Types

AND: Solution must satisfy both (intersection)
OR: Solution satisfies at least one (union)
Absolute Value: |x| < a means -a < x < a
Absolute Value: |x| > a means x < -a OR x > a