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Simplifying y[n] + 0.2y[n + -1] = x[n] + -1x[n + -1] Multiply y * n ny + 0.2y[n + -1] = x[n] + -1x[n + -1] Reorder the terms: ny + 0.2y[-1 + n] = x[n] + -1x[n + -1] ny + [-1 * 0.2y + n * 0.2y] = x[n] + -1x[n + -1] Reorder the terms: ny + [0.2ny + -0.2y] = x[n] + -1x[n + -1] ny + [0.2ny + -0.2y] = x[n] + -1x[n + -1] Combine like terms: ny + 0.2ny = 1.2ny 1.2ny + -0.2y = x[n] + -1x[n + -1] Multiply x * n 1.2ny + -0.2y = nx + -1x[n + -1] Reorder the terms: 1.2ny + -0.2y = nx + -1x[-1 + n] 1.2ny + -0.2y = nx + [-1 * -1x + n * -1x] Reorder the terms: 1.2ny + -0.2y = nx + [-1nx + 1x] 1.2ny + -0.2y = nx + [-1nx + 1x] Combine like terms: nx + -1nx = 0 1.2ny + -0.2y = 0 + 1x 1.2ny + -0.2y = 1x Solving 1.2ny + -0.2y = 1x Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '0.2y' to each side of the equation. 1.2ny + -0.2y + 0.2y = 1x + 0.2y Combine like terms: -0.2y + 0.2y = 0.0 1.2ny + 0.0 = 1x + 0.2y 1.2ny = 1x + 0.2y Divide each side by '1.2y'. n = 0.8333333333xy-1 + 0.1666666667 Simplifying n = 0.8333333333xy-1 + 0.1666666667 Reorder the terms: n = 0.1666666667 + 0.8333333333xy-1
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