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Because |u| = c means u = c or u = −c, an absolute value equation splits into two linear equations. There are two solutions when c is positive, one when c is zero and none when c is negative.
Absolute value equation
|ax + b| = c ⇒ ax + b = ±c ⇒ x = (±c − b)/a
2x − 3 = 7 gives x = 5, and 2x − 3 = −7 gives x = −2.
Absolute value measures distance from zero, which is never negative.