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Simplifying 45 + -1[4 + -2y + -4(y + 7)] = -4(1 + 3y) + -4[4 + -3(y + 2) + -2(2y + -5)] Reorder the terms: 45 + -1[4 + -2y + -4(7 + y)] = -4(1 + 3y) + -4[4 + -3(y + 2) + -2(2y + -5)] 45 + -1[4 + -2y + (7 * -4 + y * -4)] = -4(1 + 3y) + -4[4 + -3(y + 2) + -2(2y + -5)] 45 + -1[4 + -2y + (-28 + -4y)] = -4(1 + 3y) + -4[4 + -3(y + 2) + -2(2y + -5)] Reorder the terms: 45 + -1[4 + -28 + -2y + -4y] = -4(1 + 3y) + -4[4 + -3(y + 2) + -2(2y + -5)] Combine like terms: 4 + -28 = -24 45 + -1[-24 + -2y + -4y] = -4(1 + 3y) + -4[4 + -3(y + 2) + -2(2y + -5)] Combine like terms: -2y + -4y = -6y 45 + -1[-24 + -6y] = -4(1 + 3y) + -4[4 + -3(y + 2) + -2(2y + -5)] 45 + [-24 * -1 + -6y * -1] = -4(1 + 3y) + -4[4 + -3(y + 2) + -2(2y + -5)] 45 + [24 + 6y] = -4(1 + 3y) + -4[4 + -3(y + 2) + -2(2y + -5)] Combine like terms: 45 + 24 = 69 69 + 6y = -4(1 + 3y) + -4[4 + -3(y + 2) + -2(2y + -5)] 69 + 6y = (1 * -4 + 3y * -4) + -4[4 + -3(y + 2) + -2(2y + -5)] 69 + 6y = (-4 + -12y) + -4[4 + -3(y + 2) + -2(2y + -5)] Reorder the terms: 69 + 6y = -4 + -12y + -4[4 + -3(2 + y) + -2(2y + -5)] 69 + 6y = -4 + -12y + -4[4 + (2 * -3 + y * -3) + -2(2y + -5)] 69 + 6y = -4 + -12y + -4[4 + (-6 + -3y) + -2(2y + -5)] Reorder the terms: 69 + 6y = -4 + -12y + -4[4 + -6 + -3y + -2(-5 + 2y)] 69 + 6y = -4 + -12y + -4[4 + -6 + -3y + (-5 * -2 + 2y * -2)] 69 + 6y = -4 + -12y + -4[4 + -6 + -3y + (10 + -4y)] Reorder the terms: 69 + 6y = -4 + -12y + -4[4 + -6 + 10 + -3y + -4y] Combine like terms: 4 + -6 = -2 69 + 6y = -4 + -12y + -4[-2 + 10 + -3y + -4y] Combine like terms: -2 + 10 = 8 69 + 6y = -4 + -12y + -4[8 + -3y + -4y] Combine like terms: -3y + -4y = -7y 69 + 6y = -4 + -12y + -4[8 + -7y] 69 + 6y = -4 + -12y + [8 * -4 + -7y * -4] 69 + 6y = -4 + -12y + [-32 + 28y] Reorder the terms: 69 + 6y = -4 + -32 + -12y + 28y Combine like terms: -4 + -32 = -36 69 + 6y = -36 + -12y + 28y Combine like terms: -12y + 28y = 16y 69 + 6y = -36 + 16y Solving 69 + 6y = -36 + 16y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-16y' to each side of the equation. 69 + 6y + -16y = -36 + 16y + -16y Combine like terms: 6y + -16y = -10y 69 + -10y = -36 + 16y + -16y Combine like terms: 16y + -16y = 0 69 + -10y = -36 + 0 69 + -10y = -36 Add '-69' to each side of the equation. 69 + -69 + -10y = -36 + -69 Combine like terms: 69 + -69 = 0 0 + -10y = -36 + -69 -10y = -36 + -69 Combine like terms: -36 + -69 = -105 -10y = -105 Divide each side by '-10'. y = 10.5 Simplifying y = 10.5
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