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Simplifying 2(t + 3) + 9(2t + -1) = 19(t + -1) + -5 Reorder the terms: 2(3 + t) + 9(2t + -1) = 19(t + -1) + -5 (3 * 2 + t * 2) + 9(2t + -1) = 19(t + -1) + -5 (6 + 2t) + 9(2t + -1) = 19(t + -1) + -5 Reorder the terms: 6 + 2t + 9(-1 + 2t) = 19(t + -1) + -5 6 + 2t + (-1 * 9 + 2t * 9) = 19(t + -1) + -5 6 + 2t + (-9 + 18t) = 19(t + -1) + -5 Reorder the terms: 6 + -9 + 2t + 18t = 19(t + -1) + -5 Combine like terms: 6 + -9 = -3 -3 + 2t + 18t = 19(t + -1) + -5 Combine like terms: 2t + 18t = 20t -3 + 20t = 19(t + -1) + -5 Reorder the terms: -3 + 20t = 19(-1 + t) + -5 -3 + 20t = (-1 * 19 + t * 19) + -5 -3 + 20t = (-19 + 19t) + -5 Reorder the terms: -3 + 20t = -19 + -5 + 19t Combine like terms: -19 + -5 = -24 -3 + 20t = -24 + 19t Solving -3 + 20t = -24 + 19t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19t' to each side of the equation. -3 + 20t + -19t = -24 + 19t + -19t Combine like terms: 20t + -19t = 1t -3 + 1t = -24 + 19t + -19t Combine like terms: 19t + -19t = 0 -3 + 1t = -24 + 0 -3 + 1t = -24 Add '3' to each side of the equation. -3 + 3 + 1t = -24 + 3 Combine like terms: -3 + 3 = 0 0 + 1t = -24 + 3 1t = -24 + 3 Combine like terms: -24 + 3 = -21 1t = -21 Divide each side by '1'. t = -21 Simplifying t = -21
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