7(k+1)-1=7(7k)-1

Solution for 7(k+1)-1=7(7k)-1 equation:

Simplifying
7(k + 1) + -1 = 7(7k) + -1

Reorder the terms:
7(1 + k) + -1 = 7(7k) + -1
(1 * 7 + k * 7) + -1 = 7(7k) + -1
(7 + 7k) + -1 = 7(7k) + -1

Reorder the terms:
7 + -1 + 7k = 7(7k) + -1

Combine like terms: 7 + -1 = 6
6 + 7k = 7(7k) + -1

Remove parenthesis around (7k)
6 + 7k = 7 * 7k + -1

Multiply 7 * 7
6 + 7k = 49k + -1

Reorder the terms:
6 + 7k = -1 + 49k

Solving
6 + 7k = -1 + 49k

Solving for variable 'k'.

Move all terms containing k to the left, all other terms to the right.

Add '-49k' to each side of the equation.
6 + 7k + -49k = -1 + 49k + -49k

Combine like terms: 7k + -49k = -42k
6 + -42k = -1 + 49k + -49k

Combine like terms: 49k + -49k = 0
6 + -42k = -1 + 0
6 + -42k = -1

Add '-6' to each side of the equation.
6 + -6 + -42k = -1 + -6

Combine like terms: 6 + -6 = 0
0 + -42k = -1 + -6
-42k = -1 + -6

Combine like terms: -1 + -6 = -7
-42k = -7

Divide each side by '-42'.
k = 0.1666666667

Simplifying
k = 0.1666666667