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Simplifying 2(t + 1) + 3(5 + -8t) = -23(t + -2) + -8 Reorder the terms: 2(1 + t) + 3(5 + -8t) = -23(t + -2) + -8 (1 * 2 + t * 2) + 3(5 + -8t) = -23(t + -2) + -8 (2 + 2t) + 3(5 + -8t) = -23(t + -2) + -8 2 + 2t + (5 * 3 + -8t * 3) = -23(t + -2) + -8 2 + 2t + (15 + -24t) = -23(t + -2) + -8 Reorder the terms: 2 + 15 + 2t + -24t = -23(t + -2) + -8 Combine like terms: 2 + 15 = 17 17 + 2t + -24t = -23(t + -2) + -8 Combine like terms: 2t + -24t = -22t 17 + -22t = -23(t + -2) + -8 Reorder the terms: 17 + -22t = -23(-2 + t) + -8 17 + -22t = (-2 * -23 + t * -23) + -8 17 + -22t = (46 + -23t) + -8 Reorder the terms: 17 + -22t = 46 + -8 + -23t Combine like terms: 46 + -8 = 38 17 + -22t = 38 + -23t Solving 17 + -22t = 38 + -23t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '23t' to each side of the equation. 17 + -22t + 23t = 38 + -23t + 23t Combine like terms: -22t + 23t = 1t 17 + 1t = 38 + -23t + 23t Combine like terms: -23t + 23t = 0 17 + 1t = 38 + 0 17 + 1t = 38 Add '-17' to each side of the equation. 17 + -17 + 1t = 38 + -17 Combine like terms: 17 + -17 = 0 0 + 1t = 38 + -17 1t = 38 + -17 Combine like terms: 38 + -17 = 21 1t = 21 Divide each side by '1'. t = 21 Simplifying t = 21
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