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Simplifying 3(t + -1) + -5(2t + -1) = 6 + -7(5t + 3) Reorder the terms: 3(-1 + t) + -5(2t + -1) = 6 + -7(5t + 3) (-1 * 3 + t * 3) + -5(2t + -1) = 6 + -7(5t + 3) (-3 + 3t) + -5(2t + -1) = 6 + -7(5t + 3) Reorder the terms: -3 + 3t + -5(-1 + 2t) = 6 + -7(5t + 3) -3 + 3t + (-1 * -5 + 2t * -5) = 6 + -7(5t + 3) -3 + 3t + (5 + -10t) = 6 + -7(5t + 3) Reorder the terms: -3 + 5 + 3t + -10t = 6 + -7(5t + 3) Combine like terms: -3 + 5 = 2 2 + 3t + -10t = 6 + -7(5t + 3) Combine like terms: 3t + -10t = -7t 2 + -7t = 6 + -7(5t + 3) Reorder the terms: 2 + -7t = 6 + -7(3 + 5t) 2 + -7t = 6 + (3 * -7 + 5t * -7) 2 + -7t = 6 + (-21 + -35t) Combine like terms: 6 + -21 = -15 2 + -7t = -15 + -35t Solving 2 + -7t = -15 + -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. 2 + -7t + 35t = -15 + -35t + 35t Combine like terms: -7t + 35t = 28t 2 + 28t = -15 + -35t + 35t Combine like terms: -35t + 35t = 0 2 + 28t = -15 + 0 2 + 28t = -15 Add '-2' to each side of the equation. 2 + -2 + 28t = -15 + -2 Combine like terms: 2 + -2 = 0 0 + 28t = -15 + -2 28t = -15 + -2 Combine like terms: -15 + -2 = -17 28t = -17 Divide each side by '28'. t = -0.6071428571 Simplifying t = -0.6071428571
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