The second of two numbers is 6 less than the first. twice the sum of the first and 1 is the same as 9 times the second number. find the numbers.

Let x = first number
let x-6 = second number

2(x+1)=9(x-6)    distribute
2x+2=9x-54       subtract 2x from from both sides and add 54 to both sides
56=7x                divide both sides by 7
x=8