Corresponding 5585

Consider the various points corresponding to the numbers a, 2a, 3a + 1 in all possible orders on the straight line representing the number line. For each option, decide whether such an arrangement is possible. If yes, give a specific example; if not, give reasons.
Why.

Correct answer:

a₁ =  1
a₂ =  -5
a₃ =  -0.75
a₄ =  -0.25

Step-by-step explanation:

$$\begin{gathered} 2a=3a+1=>a=-1 \\ 2a=a=>a=0 \\ a=3a+1=>a=-0.5 \\ D=\{-1,-0.5,0\} \\ a,2a,3a+1 \\ {a}_1=1 \\ 1<2<4 \end{gathered}$$

$$\begin{gathered} 3a+1,2a,a \\ {a}_2=-5 \\ -14<-10<-5 \end{gathered}$$

$$\begin{gathered} 2a,3a+1,a \\ {a}_3=-0.75 \\ -1.5<-1.25<-0.75 \end{gathered}$$

$$\begin{gathered} 2a,a,3a+1 \\ {a}_4=-0.25 \\ -0.5<-0.25<0.25 \end{gathered}$$

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