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Simplifying 9(t + 9) + 6(8t + 6) = 56(t + 2) + 6 Reorder the terms: 9(9 + t) + 6(8t + 6) = 56(t + 2) + 6 (9 * 9 + t * 9) + 6(8t + 6) = 56(t + 2) + 6 (81 + 9t) + 6(8t + 6) = 56(t + 2) + 6 Reorder the terms: 81 + 9t + 6(6 + 8t) = 56(t + 2) + 6 81 + 9t + (6 * 6 + 8t * 6) = 56(t + 2) + 6 81 + 9t + (36 + 48t) = 56(t + 2) + 6 Reorder the terms: 81 + 36 + 9t + 48t = 56(t + 2) + 6 Combine like terms: 81 + 36 = 117 117 + 9t + 48t = 56(t + 2) + 6 Combine like terms: 9t + 48t = 57t 117 + 57t = 56(t + 2) + 6 Reorder the terms: 117 + 57t = 56(2 + t) + 6 117 + 57t = (2 * 56 + t * 56) + 6 117 + 57t = (112 + 56t) + 6 Reorder the terms: 117 + 57t = 112 + 6 + 56t Combine like terms: 112 + 6 = 118 117 + 57t = 118 + 56t Solving 117 + 57t = 118 + 56t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-56t' to each side of the equation. 117 + 57t + -56t = 118 + 56t + -56t Combine like terms: 57t + -56t = 1t 117 + 1t = 118 + 56t + -56t Combine like terms: 56t + -56t = 0 117 + 1t = 118 + 0 117 + 1t = 118 Add '-117' to each side of the equation. 117 + -117 + 1t = 118 + -117 Combine like terms: 117 + -117 = 0 0 + 1t = 118 + -117 1t = 118 + -117 Combine like terms: 118 + -117 = 1 1t = 1 Divide each side by '1'. t = 1 Simplifying t = 1
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