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Simplifying 49 + -1[5 + 4y + -2(y + 3)] = -4(3y + -7) + -1[6(y + -1) + -12y + 16] Reorder the terms: 49 + -1[5 + 4y + -2(3 + y)] = -4(3y + -7) + -1[6(y + -1) + -12y + 16] 49 + -1[5 + 4y + (3 * -2 + y * -2)] = -4(3y + -7) + -1[6(y + -1) + -12y + 16] 49 + -1[5 + 4y + (-6 + -2y)] = -4(3y + -7) + -1[6(y + -1) + -12y + 16] Reorder the terms: 49 + -1[5 + -6 + 4y + -2y] = -4(3y + -7) + -1[6(y + -1) + -12y + 16] Combine like terms: 5 + -6 = -1 49 + -1[-1 + 4y + -2y] = -4(3y + -7) + -1[6(y + -1) + -12y + 16] Combine like terms: 4y + -2y = 2y 49 + -1[-1 + 2y] = -4(3y + -7) + -1[6(y + -1) + -12y + 16] 49 + [-1 * -1 + 2y * -1] = -4(3y + -7) + -1[6(y + -1) + -12y + 16] 49 + [1 + -2y] = -4(3y + -7) + -1[6(y + -1) + -12y + 16] Combine like terms: 49 + 1 = 50 50 + -2y = -4(3y + -7) + -1[6(y + -1) + -12y + 16] Reorder the terms: 50 + -2y = -4(-7 + 3y) + -1[6(y + -1) + -12y + 16] 50 + -2y = (-7 * -4 + 3y * -4) + -1[6(y + -1) + -12y + 16] 50 + -2y = (28 + -12y) + -1[6(y + -1) + -12y + 16] Reorder the terms: 50 + -2y = 28 + -12y + -1[6(-1 + y) + -12y + 16] 50 + -2y = 28 + -12y + -1[(-1 * 6 + y * 6) + -12y + 16] 50 + -2y = 28 + -12y + -1[(-6 + 6y) + -12y + 16] Reorder the terms: 50 + -2y = 28 + -12y + -1[-6 + 16 + 6y + -12y] Combine like terms: -6 + 16 = 10 50 + -2y = 28 + -12y + -1[10 + 6y + -12y] Combine like terms: 6y + -12y = -6y 50 + -2y = 28 + -12y + -1[10 + -6y] 50 + -2y = 28 + -12y + [10 * -1 + -6y * -1] 50 + -2y = 28 + -12y + [-10 + 6y] Reorder the terms: 50 + -2y = 28 + -10 + -12y + 6y Combine like terms: 28 + -10 = 18 50 + -2y = 18 + -12y + 6y Combine like terms: -12y + 6y = -6y 50 + -2y = 18 + -6y Solving 50 + -2y = 18 + -6y Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6y' to each side of the equation. 50 + -2y + 6y = 18 + -6y + 6y Combine like terms: -2y + 6y = 4y 50 + 4y = 18 + -6y + 6y Combine like terms: -6y + 6y = 0 50 + 4y = 18 + 0 50 + 4y = 18 Add '-50' to each side of the equation. 50 + -50 + 4y = 18 + -50 Combine like terms: 50 + -50 = 0 0 + 4y = 18 + -50 4y = 18 + -50 Combine like terms: 18 + -50 = -32 4y = -32 Divide each side by '4'. y = -8 Simplifying y = -8
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