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Simplifying 5(t + 7) + 8(2 + -3t) = -20(t + -3) + -7 Reorder the terms: 5(7 + t) + 8(2 + -3t) = -20(t + -3) + -7 (7 * 5 + t * 5) + 8(2 + -3t) = -20(t + -3) + -7 (35 + 5t) + 8(2 + -3t) = -20(t + -3) + -7 35 + 5t + (2 * 8 + -3t * 8) = -20(t + -3) + -7 35 + 5t + (16 + -24t) = -20(t + -3) + -7 Reorder the terms: 35 + 16 + 5t + -24t = -20(t + -3) + -7 Combine like terms: 35 + 16 = 51 51 + 5t + -24t = -20(t + -3) + -7 Combine like terms: 5t + -24t = -19t 51 + -19t = -20(t + -3) + -7 Reorder the terms: 51 + -19t = -20(-3 + t) + -7 51 + -19t = (-3 * -20 + t * -20) + -7 51 + -19t = (60 + -20t) + -7 Reorder the terms: 51 + -19t = 60 + -7 + -20t Combine like terms: 60 + -7 = 53 51 + -19t = 53 + -20t Solving 51 + -19t = 53 + -20t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20t' to each side of the equation. 51 + -19t + 20t = 53 + -20t + 20t Combine like terms: -19t + 20t = 1t 51 + 1t = 53 + -20t + 20t Combine like terms: -20t + 20t = 0 51 + 1t = 53 + 0 51 + 1t = 53 Add '-51' to each side of the equation. 51 + -51 + 1t = 53 + -51 Combine like terms: 51 + -51 = 0 0 + 1t = 53 + -51 1t = 53 + -51 Combine like terms: 53 + -51 = 2 1t = 2 Divide each side by '1'. t = 2 Simplifying t = 2
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