Simple Linear Inequality Solver
This free linear inequality solver helps you solve inequalities of the form ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c.
Understanding Linear Inequalities
A linear inequality is similar to a linear equation but uses inequality symbols: <, >, ≤, ≥. Solving it means finding all x-values that satisfy the inequality.
Example: 2x + 5 < 11 → 2x < 6 → x < 3
How the Calculator Works
The calculator automatically:
Step 1: Takes values of a, b, c and the inequality sign
Step 2: Checks that a ≠ 0 (cannot divide by zero)
Step 3: Performs Step 1: subtract b from c
Step 4: Performs Step 2: divide by a, flipping the inequality if a < 0
Step 5: Displays the solution instantly
Examples
1. 3x + 4 < 10 → x < 2
2. 5x - 5 > 10 → x > 3
3. -2x + 6 ≤ 4 → x ≥ 1
4. 4x + 0 ≥ 20 → x ≥ 5
Why Linear Inequalities Matter
Linear inequalities are essential in algebra, optimization, finance, and real-world problem solving. They show ranges of solutions instead of a single value.
Common Mistakes to Avoid
- Forgetting to flip the inequality when dividing or multiplying by a negative number
- Confusing inequality symbols
- Not simplifying the equation properly before dividing
Important: When multiplying or dividing by a negative number, the inequality sign reverses direction.
Correct: For example, -2x < 4 → x > -2 (flip sign).
Frequently Asked Questions
Can a be negative?
Yes. If a < 0, the inequality sign flips after dividing.
Can I enter decimals?
Yes. Decimal coefficients and constants are supported.
What if the solution is a fraction?
The calculator displays it as a decimal; you can convert to fraction if needed.
Conclusion
Solving linear inequalities is a fundamental algebra skill. This calculator provides quick and accurate solutions for equations of the form ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c.