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Simplifying 12 + -3(2t + 1) = 7t + -3(7 + t) Reorder the terms: 12 + -3(1 + 2t) = 7t + -3(7 + t) 12 + (1 * -3 + 2t * -3) = 7t + -3(7 + t) 12 + (-3 + -6t) = 7t + -3(7 + t) Combine like terms: 12 + -3 = 9 9 + -6t = 7t + -3(7 + t) 9 + -6t = 7t + (7 * -3 + t * -3) 9 + -6t = 7t + (-21 + -3t) Reorder the terms: 9 + -6t = -21 + 7t + -3t Combine like terms: 7t + -3t = 4t 9 + -6t = -21 + 4t Solving 9 + -6t = -21 + 4t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4t' to each side of the equation. 9 + -6t + -4t = -21 + 4t + -4t Combine like terms: -6t + -4t = -10t 9 + -10t = -21 + 4t + -4t Combine like terms: 4t + -4t = 0 9 + -10t = -21 + 0 9 + -10t = -21 Add '-9' to each side of the equation. 9 + -9 + -10t = -21 + -9 Combine like terms: 9 + -9 = 0 0 + -10t = -21 + -9 -10t = -21 + -9 Combine like terms: -21 + -9 = -30 -10t = -30 Divide each side by '-10'. t = 3 Simplifying t = 3
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