Cool modulus equation
Algebra
Level
4
Find the sum of all the real solutions of the equation:
Note: If you think there are no real solutions then answer 0.
This is the part of my set Twist the Brain
The answer is 0.
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When x ≥ 2 0 2 5 ,
2 x − 3 7 5 4 = 2 9 5 ⇒ 2 x = 4 0 4 9 ⇒ x = 2 0 2 4 . 5
But, x ≥ 2 0 2 5 , so x = 2 0 2 4 . 5 is not a solution.
When x < 1 7 2 9 ,
3 7 5 4 − 2 x = 2 9 5 ⇒ 2 x = 3 4 5 9 ⇒ x = 1 7 2 9 . 5
But, x < 1 7 2 9 , so x = 1 7 2 9 . 5 is not a solution.
When x ∈ [ 1 7 2 9 , 2 0 2 5 ) ,
⇒ 1 7 2 9 − x + x − 2 0 2 5 = 2 9 5
The above statement is not true.
Hence 0 real solutions.