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IMAS 2019–2020 Junior Division — First Round Question 9

IMAS · IMAS 2019–2020 Junior Division — First Round

Question 9

Non-negative integer $x$ satisfies $|2x+5|\le15\times(1+x+x^2+\cdots+x^{2019})^0$. What is the sum of all such $x$’s?
  1. 15
  2. 25
  3. 35
  4. 45
  5. 55