Evaluate absolute values or solve simple absolute value equations such as |x − 3| = 7 with clear step-by-step results.
The absolute value of −12 is 12. For |x − 3| = 7, the two solutions are x = 10 and x = −4.
Distance from zero
- Find the distance from zero.
- Drop the negative sign if the input is negative.
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How to Use the Absolute Value Calculator
Choose whether you want to evaluate a number or solve a simple absolute value equation. For equations, enter h and k in the form |x – h| = k.
- Use evaluate mode for expressions like |-12|.
- Use solve mode for equations like |x – 3| = 7.
- Remember that absolute value represents distance.
Absolute Value Rule
Absolute value is the distance from zero on a number line. Distance cannot be negative.
For equations, |x – h| = k means x is k units away from h, so the solutions are h + k and h – k when k is nonnegative.
Absolute Value Examples
|-12|
The number -12 is 12 units from zero, so |-12| = 12.
|x – 3| = 7
The value x is 7 units from 3. The solutions are x = 10 and x = -4.
|x + 2| = 5
This is the same as |x – (-2)| = 5, so x = 3 or x = -7.
Common Absolute Value Mistakes
Returning a negative absolute value
An absolute value result is never negative when evaluating a real number.
Forgetting the second solution
Absolute value equations usually have two solutions because distance can go in two directions.
Solving when k is negative
An equation like |x – h| = -5 has no real solution because distance cannot be negative.
Absolute Value Calculator FAQs
What is absolute value?
Absolute value is the distance of a number from zero on the number line.
Why does |x – 3| = 7 have two answers?
Because x can be 7 units to the right of 3 or 7 units to the left of 3.
Can absolute value be negative?
No. Absolute value is distance, and distance is not negative.
Does this solve all absolute value equations?
This draft solves the common form |x – h| = k. More complex forms can be added later.
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Reviewer
This educational math content is reviewed under the SolverCalc reviewer rule by Prof. Dr. Khalil Mudassar. WordPress adds the author bio automatically, so this page does not include a duplicate author box.
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Disclaimer
This calculator is intended for general educational and practical use. Review important results before relying on them in professional work.