Calculadora de Equação de Valor Absoluto

This calculator solves absolute value equations in the form |ax + b| = c, where a, b, and c are real numbers provided by you. The absolute value of an expression represents its distance from zero on the number line and is always non-negative. Therefore, the calculator checks if c is greater than or equal to zero: if c is negative, the equation has no real solution. If c is zero, there is a single solution; if c is positive, there are two possible solutions.

The solution follows the principle that |ax + b| = c is equivalent to two linear equations: ax + b = c and ax + b = -c. The calculator isolates x in each case by subtracting b and dividing by a (provided a is not zero). The result is two x values that satisfy the original equation. For example, for |2x - 3| = 5, the solutions are x = 4 and x = -1.

Use this tool when you need to quickly solve absolute value equations, common in algebra problems, physics (distances, errors), and exams. It is useful for students checking their manual calculations or professionals needing fast answers. Remember to enter decimal or fractional coefficients using a dot (.) as the decimal separator.

Caution: the calculator assumes a is not zero; if a = 0, the equation reduces to |b| = c, which may have infinite solutions or none. Also, when typing values, avoid spaces and use a dot for decimals. The tool does not handle equations with more than one absolute value or variables inside other operators.