We are to solve for x in all the equations and select the ones that occur more than one solution.
Hence,
[tex]\begin{gathered} 4x-3=17 \\ 4x=17+3 \\ 4x=20 \\ x=\frac{20}{4}=5 \\ \therefore x=5 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 5(x-2)=20 \\ x-2=\frac{20}{5} \\ x-2=4 \\ x=4+2=6 \\ \therefore x=6 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 31-x=29 \\ 31-29=x \\ 2=x \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 8(x+1)=24 \\ x+1=\frac{24}{8} \\ x+1=3 \\ x=3-1=2 \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 34-7x=20 \\ 34-20=7x \\ 14=7x \\ \frac{14}{7}=\frac{7x}{7} \\ 2=x \\ \Rightarrow x=2 \end{gathered}[/tex]Lastly,
[tex]\begin{gathered} 3x+6=21 \\ 3x=21-6 \\ 3x=15 \\ x=\frac{15}{3}=5 \\ \therefore x=5 \end{gathered}[/tex]Hence, the numbers that represent solutions to more than one of the six equations are
[tex]\begin{gathered} x=2\text{ \lparen Option 2\rparen} \\ x=5\text{ \lparen Option 5\rparen} \end{gathered}[/tex]