(x+1)+(x+2)+...+(x+100)=5750
=> (x+x+.....+x)+(1+2+3+......+100)=5750
=> 100x+(100+1).100:2=5750
=> 100x+10100:2=5750
=> 100x+5050=5750
=> 100x=5750-5050
=> 100x=700
=> x=7
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