Working with the relation of "congruence modulo" is a bit hard, so lets convert this congruence modulo relations to equations.
We know that '[tex]x=1(mod 2)[/tex]' means 2 divides '[tex]x-1[/tex]'. Keep in mind I can't add a three line "equality" symbol in Brainly...
The previous can be written with this statement:
[tex]x-1=2k[/tex]
In which '[tex]k[/tex]' is any integer.
From the previous equation is very easy to see that '[tex]x=2k+1[/tex]'.
We write the remaining congruence modulo relations as equations and solve for them in similar fashion:
[tex] x_{1}-2=3k [/tex]
[tex] x_{2}-2=5k [/tex]
[tex] 2x_{3}-3=7k [/tex]
[tex] 3x_{4}-4=11k [/tex]
[tex] x_{5}-31=41k [/tex]
[tex] x_{6}-59=26k [/tex]
Now we solve for the x's, remember, k is any integer!
[tex] x_{1} =3k+2[/tex]
[tex] x_{2} =5k+2[/tex]
[tex] x_{3} = \frac{7k+3}{2} [/tex]
[tex] x_{4} = \frac{11k+4}{3} [/tex]
[tex] x_{5} =41k+31[/tex]
[tex] x_{6} =26k+59[/tex]
