If the set {x | x + a = a | x |, X ∈ r} is a single element set, then the value range of real number a is______ ．

If the set {x | x + a = a | x |, X ∈ r} is a single element set, then the value range of real number a is______ ．

When a = 0, the solution of the equation x + a = a | x | ① is x = 0, which satisfies the condition; when a ≠ 0, it is obvious that 0 is not its solution, and the solution of ① is x = AA − 1 when x > 0, and x = - AA + 1 when x < 0. The value classification of a is discussed below. When 0 < a < 1, x = AA − 1, (rounding off) x = - AA + 1 < 0 satisfies the condition; when a = 1, only one solution of ① satisfies the condition, and x = - AA + 1 satisfies the condition; when a > 1, it is obvious that the equation has two solutions, rounding off when - 1 ≤ a < 0 ① Only one root is x = AA − 1. When a ＜ - 1, there are two solutions, x = AA − 1, x = - AA + 1 (rounding off). To sum up, the range of a is - 1 ≤ a ≤ 1, so the answer is: - 1 ≤ a ≤ 1