convert a symbolic var into a numeric var

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Your sol is a list, with 1 element:

sage: sol
[x == 3]

Then, sol[0] is a symbolic expression. To get its right hand side, it suffice to use the .rhs() method:

sage: sol[0]
x == 3

sage: sol[0].rhs()
3

Then, it should be enough to work since the symbolic variable 3 should be automatically coerced by Sage into a numeric value if needed (and plot should understand symbolic numbers).

sage: sol[0].rhs().parent()
Symbolic Ring

That said, it may be a good idea to escape the symbolic ring. If you want to have a genuine integer, you can do:

sage: ZZ(sol[0].rhs())
3
sage: ZZ(sol[0].rhs()).parent()
Integer Ring

If you want an algebraic number:

sage: AA(sol[0].rhs())
3
sage: AA(sol[0].rhs()).parent()
Algebraic Real Field

If you want a floating number:

sage: RR(sol[0].rhs())
3.00000000000000
sage: RR(sol[0].rhs()).parent()
Real Field with 53 bits of precision

Here is how to plot the point:

sol=solve(2*x+1==7,x)
x0=sol[0].rhs()
point((x0,2*x0+1),size=40)