How this calculator works
A less-than comparison confines the inside expression between -c and c when c is positive. A greater-than comparison selects the two outside rays. This calculator also handles zero and negative c and constant expressions. Squaring is valid here only after treating negative c separately.
Formula
For c >= 0: |ax + b| compared with c is equivalent to (ax + b)^2 compared with c^2, using the same comparison.
Worked example
For |x - 2| < 3, subtracting the distance bound gives -3 < x - 2 < 3. Add 2 throughout to obtain -1 < x < 5, written (-1, 5).
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Frequently asked questions
Do I reverse the comparison for a negative a?
Yes when dividing an inequality by a negative value. The solver orders the endpoints after solving, so negative coefficients are supported.
What does U mean?
U joins two solution intervals. For an outside region, either interval satisfies the inequality.
Is |x| < 0 possible?
No. Its solution is the empty set, whereas |x| >= 0 holds for every real number.