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Simplifying 5(3t + 5) + 7(6t + 5) = 8(2t + -2) + -4 Reorder the terms: 5(5 + 3t) + 7(6t + 5) = 8(2t + -2) + -4 (5 * 5 + 3t * 5) + 7(6t + 5) = 8(2t + -2) + -4 (25 + 15t) + 7(6t + 5) = 8(2t + -2) + -4 Reorder the terms: 25 + 15t + 7(5 + 6t) = 8(2t + -2) + -4 25 + 15t + (5 * 7 + 6t * 7) = 8(2t + -2) + -4 25 + 15t + (35 + 42t) = 8(2t + -2) + -4 Reorder the terms: 25 + 35 + 15t + 42t = 8(2t + -2) + -4 Combine like terms: 25 + 35 = 60 60 + 15t + 42t = 8(2t + -2) + -4 Combine like terms: 15t + 42t = 57t 60 + 57t = 8(2t + -2) + -4 Reorder the terms: 60 + 57t = 8(-2 + 2t) + -4 60 + 57t = (-2 * 8 + 2t * 8) + -4 60 + 57t = (-16 + 16t) + -4 Reorder the terms: 60 + 57t = -16 + -4 + 16t Combine like terms: -16 + -4 = -20 60 + 57t = -20 + 16t Solving 60 + 57t = -20 + 16t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16t' to each side of the equation. 60 + 57t + -16t = -20 + 16t + -16t Combine like terms: 57t + -16t = 41t 60 + 41t = -20 + 16t + -16t Combine like terms: 16t + -16t = 0 60 + 41t = -20 + 0 60 + 41t = -20 Add '-60' to each side of the equation. 60 + -60 + 41t = -20 + -60 Combine like terms: 60 + -60 = 0 0 + 41t = -20 + -60 41t = -20 + -60 Combine like terms: -20 + -60 = -80 41t = -80 Divide each side by '41'. t = -1.951219512 Simplifying t = -1.951219512
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