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Simplifying y[n] + 0.5y[n + -1] = 2x[n + -1] Multiply y * n ny + 0.5y[n + -1] = 2x[n + -1] Reorder the terms: ny + 0.5y[-1 + n] = 2x[n + -1] ny + [-1 * 0.5y + n * 0.5y] = 2x[n + -1] Reorder the terms: ny + [0.5ny + -0.5y] = 2x[n + -1] ny + [0.5ny + -0.5y] = 2x[n + -1] Combine like terms: ny + 0.5ny = 1.5ny 1.5ny + -0.5y = 2x[n + -1] Reorder the terms: 1.5ny + -0.5y = 2x[-1 + n] 1.5ny + -0.5y = [-1 * 2x + n * 2x] Reorder the terms: 1.5ny + -0.5y = [2nx + -2x] 1.5ny + -0.5y = [2nx + -2x] Solving 1.5ny + -0.5y = 2nx + -2x Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2nx' to each side of the equation. 1.5ny + -2nx + -0.5y = 2nx + -2nx + -2x Reorder the terms: -2nx + 1.5ny + -0.5y = 2nx + -2nx + -2x Combine like terms: 2nx + -2nx = 0 -2nx + 1.5ny + -0.5y = 0 + -2x -2nx + 1.5ny + -0.5y = -2x Add '0.5y' to each side of the equation. -2nx + 1.5ny + -0.5y + 0.5y = -2x + 0.5y Combine like terms: -0.5y + 0.5y = 0.0 -2nx + 1.5ny + 0.0 = -2x + 0.5y -2nx + 1.5ny = -2x + 0.5y Reorder the terms: -2nx + 1.5ny + 2x + -0.5y = -2x + 2x + 0.5y + -0.5y Combine like terms: -2x + 2x = 0 -2nx + 1.5ny + 2x + -0.5y = 0 + 0.5y + -0.5y -2nx + 1.5ny + 2x + -0.5y = 0.5y + -0.5y Combine like terms: 0.5y + -0.5y = 0.0 -2nx + 1.5ny + 2x + -0.5y = 0.0 The solution to this equation could not be determined.
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