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Simplifying y[n] + 0.5y[n + -1] = x[n + -1] + 0.5x[n + -2] + -0.2x[n + -3] Multiply y * n ny + 0.5y[n + -1] = x[n + -1] + 0.5x[n + -2] + -0.2x[n + -3] Reorder the terms: ny + 0.5y[-1 + n] = x[n + -1] + 0.5x[n + -2] + -0.2x[n + -3] ny + [-1 * 0.5y + n * 0.5y] = x[n + -1] + 0.5x[n + -2] + -0.2x[n + -3] Reorder the terms: ny + [0.5ny + -0.5y] = x[n + -1] + 0.5x[n + -2] + -0.2x[n + -3] ny + [0.5ny + -0.5y] = x[n + -1] + 0.5x[n + -2] + -0.2x[n + -3] Combine like terms: ny + 0.5ny = 1.5ny 1.5ny + -0.5y = x[n + -1] + 0.5x[n + -2] + -0.2x[n + -3] Reorder the terms: 1.5ny + -0.5y = x[-1 + n] + 0.5x[n + -2] + -0.2x[n + -3] 1.5ny + -0.5y = [-1 * x + n * x] + 0.5x[n + -2] + -0.2x[n + -3] Reorder the terms: 1.5ny + -0.5y = [nx + -1x] + 0.5x[n + -2] + -0.2x[n + -3] 1.5ny + -0.5y = [nx + -1x] + 0.5x[n + -2] + -0.2x[n + -3] Reorder the terms: 1.5ny + -0.5y = nx + -1x + 0.5x[-2 + n] + -0.2x[n + -3] 1.5ny + -0.5y = nx + -1x + [-2 * 0.5x + n * 0.5x] + -0.2x[n + -3] Reorder the terms: 1.5ny + -0.5y = nx + -1x + [0.5nx + -1x] + -0.2x[n + -3] 1.5ny + -0.5y = nx + -1x + [0.5nx + -1x] + -0.2x[n + -3] Reorder the terms: 1.5ny + -0.5y = nx + -1x + 0.5nx + -1x + -0.2x[-3 + n] 1.5ny + -0.5y = nx + -1x + 0.5nx + -1x + [-3 * -0.2x + n * -0.2x] Reorder the terms: 1.5ny + -0.5y = nx + -1x + 0.5nx + -1x + [-0.2nx + 0.6x] 1.5ny + -0.5y = nx + -1x + 0.5nx + -1x + [-0.2nx + 0.6x] Reorder the terms: 1.5ny + -0.5y = nx + 0.5nx + -0.2nx + -1x + -1x + 0.6x Combine like terms: nx + 0.5nx = 1.5nx 1.5ny + -0.5y = 1.5nx + -0.2nx + -1x + -1x + 0.6x Combine like terms: 1.5nx + -0.2nx = 1.3nx 1.5ny + -0.5y = 1.3nx + -1x + -1x + 0.6x Combine like terms: -1x + -1x = -2x 1.5ny + -0.5y = 1.3nx + -2x + 0.6x Combine like terms: -2x + 0.6x = -1.4x 1.5ny + -0.5y = 1.3nx + -1.4x Solving 1.5ny + -0.5y = 1.3nx + -1.4x Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-1.3nx' to each side of the equation. 1.5ny + -1.3nx + -0.5y = 1.3nx + -1.3nx + -1.4x Reorder the terms: -1.3nx + 1.5ny + -0.5y = 1.3nx + -1.3nx + -1.4x Combine like terms: 1.3nx + -1.3nx = 0.0 -1.3nx + 1.5ny + -0.5y = 0.0 + -1.4x -1.3nx + 1.5ny + -0.5y = -1.4x Add '0.5y' to each side of the equation. -1.3nx + 1.5ny + -0.5y + 0.5y = -1.4x + 0.5y Combine like terms: -0.5y + 0.5y = 0.0 -1.3nx + 1.5ny + 0.0 = -1.4x + 0.5y -1.3nx + 1.5ny = -1.4x + 0.5y Reorder the terms: -1.3nx + 1.5ny + 1.4x + -0.5y = -1.4x + 1.4x + 0.5y + -0.5y Combine like terms: -1.4x + 1.4x = 0.0 -1.3nx + 1.5ny + 1.4x + -0.5y = 0.0 + 0.5y + -0.5y -1.3nx + 1.5ny + 1.4x + -0.5y = 0.5y + -0.5y Combine like terms: 0.5y + -0.5y = 0.0 -1.3nx + 1.5ny + 1.4x + -0.5y = 0.0 The solution to this equation could not be determined.
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