Integer

Find the integer whose distance on the numerical axis from number 1 is two times smaller as the distance from number 6.

Result

x =  -4

Solution:

∣x−1∣=∣x−6∣/2  x...(−inf,1)  −(a−1)=−(a−6)/2  a=−4  a=−4  x......(1,6)  (b−1)=−(b−6)/2  3b=8  b=83≐2.666667  x......(6,+inf)  (c−1)=(c−6)/2  c=−4  c=−4   x=a=(−4)=−4|x-1|=|x-6|/2 \ \\ \ \\ x ... (-inf, 1) \ \\ \ \\ -(a-1)=-(a-6)/2 \ \\ \ \\ a=-4 \ \\ \ \\ a=-4 \ \\ \ \\ x ...... (1,6) \ \\ \ \\ (b-1)=-(b-6)/2 \ \\ \ \\ 3b=8 \ \\ \ \\ b=\dfrac{ 8 }{ 3 } \doteq 2.666667 \ \\ \ \\ x ...... (6,+inf) \ \\ \ \\ (c-1)=(c-6)/2 \ \\ \ \\ c=-4 \ \\ \ \\ c=-4 \ \\ \ \\ \ \\ x=a=(-4)=-4

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