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Simplifying -3(t + 9) + 7(2t + 8) = 10(t + 2) + 7 Reorder the terms: -3(9 + t) + 7(2t + 8) = 10(t + 2) + 7 (9 * -3 + t * -3) + 7(2t + 8) = 10(t + 2) + 7 (-27 + -3t) + 7(2t + 8) = 10(t + 2) + 7 Reorder the terms: -27 + -3t + 7(8 + 2t) = 10(t + 2) + 7 -27 + -3t + (8 * 7 + 2t * 7) = 10(t + 2) + 7 -27 + -3t + (56 + 14t) = 10(t + 2) + 7 Reorder the terms: -27 + 56 + -3t + 14t = 10(t + 2) + 7 Combine like terms: -27 + 56 = 29 29 + -3t + 14t = 10(t + 2) + 7 Combine like terms: -3t + 14t = 11t 29 + 11t = 10(t + 2) + 7 Reorder the terms: 29 + 11t = 10(2 + t) + 7 29 + 11t = (2 * 10 + t * 10) + 7 29 + 11t = (20 + 10t) + 7 Reorder the terms: 29 + 11t = 20 + 7 + 10t Combine like terms: 20 + 7 = 27 29 + 11t = 27 + 10t Solving 29 + 11t = 27 + 10t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10t' to each side of the equation. 29 + 11t + -10t = 27 + 10t + -10t Combine like terms: 11t + -10t = 1t 29 + 1t = 27 + 10t + -10t Combine like terms: 10t + -10t = 0 29 + 1t = 27 + 0 29 + 1t = 27 Add '-29' to each side of the equation. 29 + -29 + 1t = 27 + -29 Combine like terms: 29 + -29 = 0 0 + 1t = 27 + -29 1t = 27 + -29 Combine like terms: 27 + -29 = -2 1t = -2 Divide each side by '1'. t = -2 Simplifying t = -2
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