(5)(r+9)-(2)(1-r)=1

Solution for (5)(r+9)-(2)(1-r)=1 equation:

Simplifying
(5)(r + 9) + -1(2)(1 + -1r) = 1

Reorder the terms:
5(9 + r) + -1(2)(1 + -1r) = 1
(9 * 5 + r * 5) + -1(2)(1 + -1r) = 1
(45 + 5r) + -1(2)(1 + -1r) = 1

Multiply -1 * 2
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