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Simplifying 55 + -1[5 + 4y + -2(y + 3)] = -4(5y + -3) + -1[6(y + -1) + -16y + 2] Reorder the terms: 55 + -1[5 + 4y + -2(3 + y)] = -4(5y + -3) + -1[6(y + -1) + -16y + 2] 55 + -1[5 + 4y + (3 * -2 + y * -2)] = -4(5y + -3) + -1[6(y + -1) + -16y + 2] 55 + -1[5 + 4y + (-6 + -2y)] = -4(5y + -3) + -1[6(y + -1) + -16y + 2] Reorder the terms: 55 + -1[5 + -6 + 4y + -2y] = -4(5y + -3) + -1[6(y + -1) + -16y + 2] Combine like terms: 5 + -6 = -1 55 + -1[-1 + 4y + -2y] = -4(5y + -3) + -1[6(y + -1) + -16y + 2] Combine like terms: 4y + -2y = 2y 55 + -1[-1 + 2y] = -4(5y + -3) + -1[6(y + -1) + -16y + 2] 55 + [-1 * -1 + 2y * -1] = -4(5y + -3) + -1[6(y + -1) + -16y + 2] 55 + [1 + -2y] = -4(5y + -3) + -1[6(y + -1) + -16y + 2] Combine like terms: 55 + 1 = 56 56 + -2y = -4(5y + -3) + -1[6(y + -1) + -16y + 2] Reorder the terms: 56 + -2y = -4(-3 + 5y) + -1[6(y + -1) + -16y + 2] 56 + -2y = (-3 * -4 + 5y * -4) + -1[6(y + -1) + -16y + 2] 56 + -2y = (12 + -20y) + -1[6(y + -1) + -16y + 2] Reorder the terms: 56 + -2y = 12 + -20y + -1[6(-1 + y) + -16y + 2] 56 + -2y = 12 + -20y + -1[(-1 * 6 + y * 6) + -16y + 2] 56 + -2y = 12 + -20y + -1[(-6 + 6y) + -16y + 2] Reorder the terms: 56 + -2y = 12 + -20y + -1[-6 + 2 + 6y + -16y] Combine like terms: -6 + 2 = -4 56 + -2y = 12 + -20y + -1[-4 + 6y + -16y] Combine like terms: 6y + -16y = -10y 56 + -2y = 12 + -20y + -1[-4 + -10y] 56 + -2y = 12 + -20y + [-4 * -1 + -10y * -1] 56 + -2y = 12 + -20y + [4 + 10y] Reorder the terms: 56 + -2y = 12 + 4 + -20y + 10y Combine like terms: 12 + 4 = 16 56 + -2y = 16 + -20y + 10y Combine like terms: -20y + 10y = -10y 56 + -2y = 16 + -10y Solving 56 + -2y = 16 + -10y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10y' to each side of the equation. 56 + -2y + 10y = 16 + -10y + 10y Combine like terms: -2y + 10y = 8y 56 + 8y = 16 + -10y + 10y Combine like terms: -10y + 10y = 0 56 + 8y = 16 + 0 56 + 8y = 16 Add '-56' to each side of the equation. 56 + -56 + 8y = 16 + -56 Combine like terms: 56 + -56 = 0 0 + 8y = 16 + -56 8y = 16 + -56 Combine like terms: 16 + -56 = -40 8y = -40 Divide each side by '8'. y = -5 Simplifying y = -5
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