Integer

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

Correct answer:

x =  -4

Step-by-step explanation:

$$\begin{gathered} \mathrm{\mid }x-1\mathrm{\mid }=\mathrm{\mid }x-6\mathrm{\mid }\mathrm{/}2 \\ x\dots (-inf,1) \\ -(a-1)=-(a-6)\mathrm{/}2 \\ a=-4 \\ x\dots \dots (1,6) \\ (b-1)=-(b-6)\mathrm{/}2 \\ 3b=8 \\ b={\displaystyle \frac{8}{3}}\doteq 2.666667 \\ x\dots \dots (6,+inf) \\ (c-1)=(c-6)\mathrm{/}2 \\ c=-4 \\ x=a=(-4)=-4 \end{gathered}$$

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