Absolute Value Equation Solver

Easily solve equations of the form $$|ax + b| = c$$ and visualize the solutions.

Equation Parameters

Enter the coefficients for the absolute value equation $$|ax + b| = c$$.

Solutions

x1 ≈ x2 ≈

Visualization

Understanding Absolute Value Equations

An absolute value equation involves the absolute value of a variable expression. The absolute value of a number is its distance from zero, always non-negative. For example, $$|x| = 3$$ has two solutions: $$x = 3$$ and $$x = -3$$, because both 3 and -3 are 3 units away from zero.

To solve $$|ax + b| = c$$, we consider two cases:

  1. $$ax + b = c$$
  2. $$ax + b = -c$$
Solving these linear equations gives the possible values for x. This tool helps you find these solutions and visualize them graphically, showing where the function $$y = |ax + b|$$ intersects with the line $$y = c$$.

Learn more about absolute values on resources like Math is Fun and Wikipedia.