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Simplifying -7(t + 6) + 5(8 + -2t) = -18(t + -1) + -8 Reorder the terms: -7(6 + t) + 5(8 + -2t) = -18(t + -1) + -8 (6 * -7 + t * -7) + 5(8 + -2t) = -18(t + -1) + -8 (-42 + -7t) + 5(8 + -2t) = -18(t + -1) + -8 -42 + -7t + (8 * 5 + -2t * 5) = -18(t + -1) + -8 -42 + -7t + (40 + -10t) = -18(t + -1) + -8 Reorder the terms: -42 + 40 + -7t + -10t = -18(t + -1) + -8 Combine like terms: -42 + 40 = -2 -2 + -7t + -10t = -18(t + -1) + -8 Combine like terms: -7t + -10t = -17t -2 + -17t = -18(t + -1) + -8 Reorder the terms: -2 + -17t = -18(-1 + t) + -8 -2 + -17t = (-1 * -18 + t * -18) + -8 -2 + -17t = (18 + -18t) + -8 Reorder the terms: -2 + -17t = 18 + -8 + -18t Combine like terms: 18 + -8 = 10 -2 + -17t = 10 + -18t Solving -2 + -17t = 10 + -18t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18t' to each side of the equation. -2 + -17t + 18t = 10 + -18t + 18t Combine like terms: -17t + 18t = 1t -2 + 1t = 10 + -18t + 18t Combine like terms: -18t + 18t = 0 -2 + 1t = 10 + 0 -2 + 1t = 10 Add '2' to each side of the equation. -2 + 2 + 1t = 10 + 2 Combine like terms: -2 + 2 = 0 0 + 1t = 10 + 2 1t = 10 + 2 Combine like terms: 10 + 2 = 12 1t = 12 Divide each side by '1'. t = 12 Simplifying t = 12
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