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Simplifying 2(t + -1) + -3(3t + -2) = 12 + -5(7t + 5) Reorder the terms: 2(-1 + t) + -3(3t + -2) = 12 + -5(7t + 5) (-1 * 2 + t * 2) + -3(3t + -2) = 12 + -5(7t + 5) (-2 + 2t) + -3(3t + -2) = 12 + -5(7t + 5) Reorder the terms: -2 + 2t + -3(-2 + 3t) = 12 + -5(7t + 5) -2 + 2t + (-2 * -3 + 3t * -3) = 12 + -5(7t + 5) -2 + 2t + (6 + -9t) = 12 + -5(7t + 5) Reorder the terms: -2 + 6 + 2t + -9t = 12 + -5(7t + 5) Combine like terms: -2 + 6 = 4 4 + 2t + -9t = 12 + -5(7t + 5) Combine like terms: 2t + -9t = -7t 4 + -7t = 12 + -5(7t + 5) Reorder the terms: 4 + -7t = 12 + -5(5 + 7t) 4 + -7t = 12 + (5 * -5 + 7t * -5) 4 + -7t = 12 + (-25 + -35t) Combine like terms: 12 + -25 = -13 4 + -7t = -13 + -35t Solving 4 + -7t = -13 + -35t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35t' to each side of the equation. 4 + -7t + 35t = -13 + -35t + 35t Combine like terms: -7t + 35t = 28t 4 + 28t = -13 + -35t + 35t Combine like terms: -35t + 35t = 0 4 + 28t = -13 + 0 4 + 28t = -13 Add '-4' to each side of the equation. 4 + -4 + 28t = -13 + -4 Combine like terms: 4 + -4 = 0 0 + 28t = -13 + -4 28t = -13 + -4 Combine like terms: -13 + -4 = -17 28t = -17 Divide each side by '28'. t = -0.6071428571 Simplifying t = -0.6071428571
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