Math

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Absolute Value Equation Calculator.

Solve |x| = a and display both real roots.

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Set your values

Results update as you type.

Positive root: 5

Positive root

5.000000
Negative root: -5

Negative root

-5.000000

Results update automatically as you type.

Use Cases

Quickly solve basic absolute value equations

Ideal for students or anyone needing to find the solutions to |x| = a without manual calculation. It provides both roots instantly, saving time and reducing errors.

Example: Enter 7 to get x = 7 and x = -7.

Check your manual solutions

Use this calculator to verify your own work when solving absolute value equations. It's a reliable reference for confirming the correct roots.

Example: After solving |x| = 12 by hand, check that the calculator gives 12 and -12.

Frequently Asked Questions

How do I use the Absolute Value Equation Calculator?
Enter the value of 'a' (the right-hand side of the equation |x| = a) into the input field. The calculator will then solve for x and display both real roots: x = a and x = -a. If a is negative, there are no real solutions.
What does the calculator display as the solution?
It displays both real roots of the equation |x| = a. For a positive 'a', the roots are a and -a. For a = 0, the only root is 0. For negative 'a', there are no real solutions because the absolute value cannot be negative.
Can this calculator handle equations like |2x - 3| = 5?
No, this calculator is specifically designed for the simple form |x| = a, where the variable is alone inside the absolute value. For more complex equations, you would need a different tool.

Tips & Common Mistakes

Tips

  • Remember that the absolute value of a number is always non-negative. So if you enter a negative number for 'a', there will be no real solutions.
  • When 'a' is zero, the equation |x| = 0 has exactly one solution: x = 0. The calculator will display that.
  • For any positive 'a', the two solutions are always opposites: a and -a. This is because absolute value measures distance from zero.
  • Use this calculator as a quick check for homework or practice problems, but also understand the concept to solve more complex equations.

Common Mistakes to Avoid

  • Forgetting that there are two solutions for positive 'a'. Many people only give the positive root, but the negative root is equally valid.
  • Thinking that a negative 'a' can have solutions. Since absolute value is never negative, |x| = -5 has no real solution.
  • Confusing the right-hand side value with the variable. The input field is for 'a', not for 'x'.

Last updated: August 13, 2026