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Simplifying -2(t + -1) + -8(3t + -3) = -27(t + -2) + -3 Reorder the terms: -2(-1 + t) + -8(3t + -3) = -27(t + -2) + -3 (-1 * -2 + t * -2) + -8(3t + -3) = -27(t + -2) + -3 (2 + -2t) + -8(3t + -3) = -27(t + -2) + -3 Reorder the terms: 2 + -2t + -8(-3 + 3t) = -27(t + -2) + -3 2 + -2t + (-3 * -8 + 3t * -8) = -27(t + -2) + -3 2 + -2t + (24 + -24t) = -27(t + -2) + -3 Reorder the terms: 2 + 24 + -2t + -24t = -27(t + -2) + -3 Combine like terms: 2 + 24 = 26 26 + -2t + -24t = -27(t + -2) + -3 Combine like terms: -2t + -24t = -26t 26 + -26t = -27(t + -2) + -3 Reorder the terms: 26 + -26t = -27(-2 + t) + -3 26 + -26t = (-2 * -27 + t * -27) + -3 26 + -26t = (54 + -27t) + -3 Reorder the terms: 26 + -26t = 54 + -3 + -27t Combine like terms: 54 + -3 = 51 26 + -26t = 51 + -27t Solving 26 + -26t = 51 + -27t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '27t' to each side of the equation. 26 + -26t + 27t = 51 + -27t + 27t Combine like terms: -26t + 27t = 1t 26 + 1t = 51 + -27t + 27t Combine like terms: -27t + 27t = 0 26 + 1t = 51 + 0 26 + 1t = 51 Add '-26' to each side of the equation. 26 + -26 + 1t = 51 + -26 Combine like terms: 26 + -26 = 0 0 + 1t = 51 + -26 1t = 51 + -26 Combine like terms: 51 + -26 = 25 1t = 25 Divide each side by '1'. t = 25 Simplifying t = 25
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