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Simplifying 2(t + 3) + -1(3t + -1) = 4(-2t + 3) + -6 Reorder the terms: 2(3 + t) + -1(3t + -1) = 4(-2t + 3) + -6 (3 * 2 + t * 2) + -1(3t + -1) = 4(-2t + 3) + -6 (6 + 2t) + -1(3t + -1) = 4(-2t + 3) + -6 Reorder the terms: 6 + 2t + -1(-1 + 3t) = 4(-2t + 3) + -6 6 + 2t + (-1 * -1 + 3t * -1) = 4(-2t + 3) + -6 6 + 2t + (1 + -3t) = 4(-2t + 3) + -6 Reorder the terms: 6 + 1 + 2t + -3t = 4(-2t + 3) + -6 Combine like terms: 6 + 1 = 7 7 + 2t + -3t = 4(-2t + 3) + -6 Combine like terms: 2t + -3t = -1t 7 + -1t = 4(-2t + 3) + -6 Reorder the terms: 7 + -1t = 4(3 + -2t) + -6 7 + -1t = (3 * 4 + -2t * 4) + -6 7 + -1t = (12 + -8t) + -6 Reorder the terms: 7 + -1t = 12 + -6 + -8t Combine like terms: 12 + -6 = 6 7 + -1t = 6 + -8t Solving 7 + -1t = 6 + -8t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8t' to each side of the equation. 7 + -1t + 8t = 6 + -8t + 8t Combine like terms: -1t + 8t = 7t 7 + 7t = 6 + -8t + 8t Combine like terms: -8t + 8t = 0 7 + 7t = 6 + 0 7 + 7t = 6 Add '-7' to each side of the equation. 7 + -7 + 7t = 6 + -7 Combine like terms: 7 + -7 = 0 0 + 7t = 6 + -7 7t = 6 + -7 Combine like terms: 6 + -7 = -1 7t = -1 Divide each side by '7'. t = -0.1428571429 Simplifying t = -0.1428571429
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