Linear modulus inequalities with constant bounds

For c>0, |u| <= c -c <= u <= c. For c 0, |u|>c u<-c or u>c. These describe inside and outside a distance band. Divide a positive outside multiplier first. Use a joined pair of inequalities for the inside band, separate alternatives for the outside band, and retain the endpoint symbols. 2|x-1| 6 becomes -3 <= x-1 3, hence -2 <= x 4. Check: outside means OR, not AND. When the bound is zero, |u|>0 excludes only the zeros; it does not exclude all negative inner values.