Calculadora de Desigualdades em Reta Numérica
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
ax + b < c ⇔ x < (c−b)/a (se a > 0)
About this calculator
The Number Line Inequality Calculator solves linear inequalities of the form ax + b < c, providing the critical value of x. The result indicates on which interval of the number line the inequality holds true. For example, for 2x + 3 < 7, the calculator returns x < 2, showing that all numbers less than 2 satisfy the condition.
How it works: the calculator applies the formula x < (c - b) / a when a > 0. If a is negative, the inequality sign is reversed. The result is displayed on a number line, highlighting the solution interval. This tool is useful for algebra students, teachers, and professionals who need to quickly solve linear inequalities.
When to use? Ideal for checking math exercises, preparing lessons, or solving problems involving value ranges. For example, determining the temperature range for a safe chemical process, or calculating budget limits. The calculator streamlines this process, avoiding manual errors.
Cautions: Check if the calculator correctly handles sign reversal when a is negative. Also, remember that the formula assumes a ≠ 0. For nonlinear inequalities or systems, other tools are needed. Always verify the result with simple tests.
Frequently asked questions
What happens if the coefficient 'a' is negative?
If 'a' is negative, the inequality ax + b < c becomes x > (c - b)/a, because the sign is reversed when dividing by a negative number.
What if 'a' equals zero?
If a = 0, the inequality reduces to b < c, which is either true or false regardless of x. The calculator does not handle this case, as the formula requires a ≠ 0.
Can I use it for inequalities with ≥ or >?
This specific calculator solves only ax + b < c. For other types, you need a different tool or adjust manually.
How does the calculator display the result?
The result is shown as an interval on the number line, e.g., x < 2, with an open circle at the critical value indicating it is not included.
Does it work with decimals and fractions?
Yes, you can input decimals and fractions. The calculator processes all real numbers, as long as a ≠ 0.