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