Number line

Find a number on the number line whose distance from the number 3 is four times smaller than from the number 15 (specify both solutions).

Correct answer:

a₁ =  5.4
a₂ =  -1

Step-by-step explanation:

$$\begin{gathered} |a-3|=|a-15|/4 \\ a>15 \\ (x-3)=(x-15)/4 \\ 3x=-3 \\ x=\frac{-3}{3}=-1 \\ x=-1 \\ a\in <3;15> \\ {a}_1-3=(15-a_1)/4 \\ 5a_1=27 \\ {a}_1=\frac{27}{5}=5.4 \\ {a}_1=\frac{27}{5}=5.4 \end{gathered}$$

$$\begin{gathered} a<3 \\ 3-a_2=(15-a_2)/4 \\ 3a_2=-3 \\ {a}_2=\frac{-3}{3}=-1 \\ {a}_2=-1 \end{gathered}$$

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