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Simplifying -3(t + -8) + 7(3t + 2) = 17(t + 2) + 1 Reorder the terms: -3(-8 + t) + 7(3t + 2) = 17(t + 2) + 1 (-8 * -3 + t * -3) + 7(3t + 2) = 17(t + 2) + 1 (24 + -3t) + 7(3t + 2) = 17(t + 2) + 1 Reorder the terms: 24 + -3t + 7(2 + 3t) = 17(t + 2) + 1 24 + -3t + (2 * 7 + 3t * 7) = 17(t + 2) + 1 24 + -3t + (14 + 21t) = 17(t + 2) + 1 Reorder the terms: 24 + 14 + -3t + 21t = 17(t + 2) + 1 Combine like terms: 24 + 14 = 38 38 + -3t + 21t = 17(t + 2) + 1 Combine like terms: -3t + 21t = 18t 38 + 18t = 17(t + 2) + 1 Reorder the terms: 38 + 18t = 17(2 + t) + 1 38 + 18t = (2 * 17 + t * 17) + 1 38 + 18t = (34 + 17t) + 1 Reorder the terms: 38 + 18t = 34 + 1 + 17t Combine like terms: 34 + 1 = 35 38 + 18t = 35 + 17t Solving 38 + 18t = 35 + 17t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-17t' to each side of the equation. 38 + 18t + -17t = 35 + 17t + -17t Combine like terms: 18t + -17t = 1t 38 + 1t = 35 + 17t + -17t Combine like terms: 17t + -17t = 0 38 + 1t = 35 + 0 38 + 1t = 35 Add '-38' to each side of the equation. 38 + -38 + 1t = 35 + -38 Combine like terms: 38 + -38 = 0 0 + 1t = 35 + -38 1t = 35 + -38 Combine like terms: 35 + -38 = -3 1t = -3 Divide each side by '1'. t = -3 Simplifying t = -3
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