Because |a| is the distance of the point a from the origin on the real line, the equation:
is true if either a = b or a = -b. Similarly, the equation:|a| = b
is also true if either a = b or a = -b. That is, there may be two solutions for a.|a| = |b|
Example, solve: |x + 2| = 1
x + 2 = 1 or x + 2 = -1
x = -1 or x = -3
Solution set: {-3, -1}
Example, solve: |x + 3| = |2x - 1|
x + 3 = 2x - 1 or x + 3 = -2x + 1
4 = x or 3x = -2
x = 4 or x = -2/3
Solution set: {-2/3, 4}