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Simplifying x(n + 1) = 1 + 4x(n) Reorder the terms: x(1 + n) = 1 + 4x(n) (1 * x + n * x) = 1 + 4x(n) Reorder the terms: (nx + 1x) = 1 + 4x(n) (nx + 1x) = 1 + 4x(n) Multiply x * n nx + 1x = 1 + 4nx Solving nx + 1x = 1 + 4nx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4nx' to each side of the equation. nx + -4nx + 1x = 1 + 4nx + -4nx Combine like terms: nx + -4nx = -3nx -3nx + 1x = 1 + 4nx + -4nx Combine like terms: 4nx + -4nx = 0 -3nx + 1x = 1 + 0 -3nx + 1x = 1 Add '-1x' to each side of the equation. -3nx + 1x + -1x = 1 + -1x Combine like terms: 1x + -1x = 0 -3nx + 0 = 1 + -1x -3nx = 1 + -1x Divide each side by '-3x'. n = -0.3333333333x-1 + 0.3333333333 Simplifying n = -0.3333333333x-1 + 0.3333333333 Reorder the terms: n = 0.3333333333 + -0.3333333333x-1
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