Algebra 1 Basic

Linear Inequalities

Solve and graph linear and compound inequalities with interval notation and number line visualization.

Live Calculator · Step-by-Step · Algebra 1
Inequality Setup
Use <, >, <=, >=, ≤, or ≥. Supports fractions: (x+1)/2 > 3.
Examples
AND form: a < bx+c < d  |  OR form: expr1 OR expr2 (use "OR" or "or").
Examples
Solution
Enter an inequality above and press Solve & Graph to see the solution, interval notation, and number line.
Solution (Inequality)
Interval Notation
Step-by-Step Solution
Number Line
Inequality Rules
Solve like an equation — with one key exception

Addition / Subtraction: Add or subtract the same value from both sides — the inequality direction stays the same.

Multiply / Divide by a positive: The inequality direction stays the same.

Multiply / Divide by a negative: The inequality sign FLIPS.

3x < 9 → x < 3  (divide by +3, no flip)

−3x < 9 → x > −3  (divide by −3, FLIP!)

When you multiply or divide both sides by a negative number, always flip the inequality sign (e.g. < becomes >).
Interval Notation
( ) = open (strict)  |  [ ] = closed (includes)
InequalityInterval Notation
x < a(-∞, a)
x ≤ a(-∞, a]
x > a(a, ∞)
x ≥ a[a, ∞)
a < x < b(a, b)
a ≤ x ≤ b[a, b]
x < a OR x > b(-∞, a) ∪ (b, ∞)

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