5[r+9]-2[1-r]=1

Solution for 5[r+9]-2[1-r]=1 equation:

Simplifying
5[r + 9] + -2[1 + -1r] = 1

Reorder the terms:
5[9 + r] + -2[1 + -1r] = 1
[9 * 5 + r * 5] + -2[1 + -1r] = 1
[45 + 5r] + -2[1 + -1r] = 1
45 + 5r + [1 * -2 + -1r * -2] = 1
45 + 5r + [-2 + 2r] = 1

Reorder the terms:
45 + -2 + 5r + 2r = 1

Combine like terms: 45 + -2 = 43
43 + 5r + 2r = 1

Combine like terms: 5r + 2r = 7r
43 + 7r = 1

Solving
43 + 7r = 1

Solving for variable 'r'.

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

Add '-43' to each side of the equation.
43 + -43 + 7r = 1 + -43

Combine like terms: 43 + -43 = 0
0 + 7r = 1 + -43
7r = 1 + -43

Combine like terms: 1 + -43 = -42
7r = -42

Divide each side by '7'.
r = -6

Simplifying
r = -6