Linear modulus equations with constant targets

For c 0, |u|=c means u=c or u=-c. These are the two points at distance c from zero. Isolate the modulus, solve both linear equations, remove duplicates and check the original equation and any domain. For |2x+1|=3, solve 2x+1=+-3: x=1,-2. Both are valid. Check: when c=0, the sign equations are identical. A negative target has no solution because absolute values are nonnegative.