The distance in a coordinate line is given by:
[tex]d(A,B)=\lvert B-A\rvert[/tex]
in this case we know that A=-6 and we would like to know the value of B so that the distance is 20. Plugging this values in the equation we have:
[tex]\begin{gathered} \lvert B-(-6)\rvert=20 \\ \lvert B+6\rvert=20 \end{gathered}[/tex]
Now we need to remember the property:
[tex]\begin{gathered} \lvert x\rvert=a \\ \text{implies} \\ x=\pm a \end{gathered}[/tex]
Using this we have:
[tex]\begin{gathered} \lvert B+6\rvert=20 \\ B+6=\pm20 \\ B=-6\pm20 \end{gathered}[/tex]
Then:
[tex]\begin{gathered} B=-6+20=14 \\ B=-6-20=-26 \end{gathered}[/tex]
Therefore the two possible coordinates for B are 14 and -26.
