Absolute Value Equation Calculator

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Choose equation to find exact roots; choose an inequality to find the solution interval.
The number multiplying x inside the absolute value bars. For |x + 3| = 5, a = 1.
The constant added to ax inside the absolute value bars. For |2x - 1| = 7, b = -1.
A number added to the absolute value expression on the left side. For |2x+3| + 1 = 8, c = 1. Set to 0 if there is no outside constant.
The value on the right side of the equation or inequality. For |2x+3| = 7, d = 7.
Solution typeSolution found
Two solutions

Whether the equation has two, one, or no real solutions.

Solution x₁x = 2
Solution x₂x = -5
Isolated |ax+b|7
Solution x₁-5
Solution x₂2

Result: Two solutions.

  • The equation |2x + 3| = 7 splits into two linear equations: 2x + 3 = 7 and 2x + 3 = -7.
  • Both solutions must be verified by substituting back; absolute value equations can produce extraneous roots if d - c is incorrectly negative.
  • The two solutions are symmetric around x = -3/2, which is where |2x + 3| = 0.

Next stepVerify each solution by substituting it back into the original equation. If the result equals d, the solution is valid.

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