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Simplifying 22 + -1[5 + 6y + -2(y + 2)] = -4(3y + -7) + -1[9(y + -1) + -15y + 24] Reorder the terms: 22 + -1[5 + 6y + -2(2 + y)] = -4(3y + -7) + -1[9(y + -1) + -15y + 24] 22 + -1[5 + 6y + (2 * -2 + y * -2)] = -4(3y + -7) + -1[9(y + -1) + -15y + 24] 22 + -1[5 + 6y + (-4 + -2y)] = -4(3y + -7) + -1[9(y + -1) + -15y + 24] Reorder the terms: 22 + -1[5 + -4 + 6y + -2y] = -4(3y + -7) + -1[9(y + -1) + -15y + 24] Combine like terms: 5 + -4 = 1 22 + -1[1 + 6y + -2y] = -4(3y + -7) + -1[9(y + -1) + -15y + 24] Combine like terms: 6y + -2y = 4y 22 + -1[1 + 4y] = -4(3y + -7) + -1[9(y + -1) + -15y + 24] 22 + [1 * -1 + 4y * -1] = -4(3y + -7) + -1[9(y + -1) + -15y + 24] 22 + [-1 + -4y] = -4(3y + -7) + -1[9(y + -1) + -15y + 24] Combine like terms: 22 + -1 = 21 21 + -4y = -4(3y + -7) + -1[9(y + -1) + -15y + 24] Reorder the terms: 21 + -4y = -4(-7 + 3y) + -1[9(y + -1) + -15y + 24] 21 + -4y = (-7 * -4 + 3y * -4) + -1[9(y + -1) + -15y + 24] 21 + -4y = (28 + -12y) + -1[9(y + -1) + -15y + 24] Reorder the terms: 21 + -4y = 28 + -12y + -1[9(-1 + y) + -15y + 24] 21 + -4y = 28 + -12y + -1[(-1 * 9 + y * 9) + -15y + 24] 21 + -4y = 28 + -12y + -1[(-9 + 9y) + -15y + 24] Reorder the terms: 21 + -4y = 28 + -12y + -1[-9 + 24 + 9y + -15y] Combine like terms: -9 + 24 = 15 21 + -4y = 28 + -12y + -1[15 + 9y + -15y] Combine like terms: 9y + -15y = -6y 21 + -4y = 28 + -12y + -1[15 + -6y] 21 + -4y = 28 + -12y + [15 * -1 + -6y * -1] 21 + -4y = 28 + -12y + [-15 + 6y] Reorder the terms: 21 + -4y = 28 + -15 + -12y + 6y Combine like terms: 28 + -15 = 13 21 + -4y = 13 + -12y + 6y Combine like terms: -12y + 6y = -6y 21 + -4y = 13 + -6y Solving 21 + -4y = 13 + -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. 21 + -4y + 6y = 13 + -6y + 6y Combine like terms: -4y + 6y = 2y 21 + 2y = 13 + -6y + 6y Combine like terms: -6y + 6y = 0 21 + 2y = 13 + 0 21 + 2y = 13 Add '-21' to each side of the equation. 21 + -21 + 2y = 13 + -21 Combine like terms: 21 + -21 = 0 0 + 2y = 13 + -21 2y = 13 + -21 Combine like terms: 13 + -21 = -8 2y = -8 Divide each side by '2'. y = -4 Simplifying y = -4
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