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Simplifying 3(5 + 3t) + -1(1 + -1t) + 4(6 + 4t) = 12 (5 * 3 + 3t * 3) + -1(1 + -1t) + 4(6 + 4t) = 12 (15 + 9t) + -1(1 + -1t) + 4(6 + 4t) = 12 15 + 9t + (1 * -1 + -1t * -1) + 4(6 + 4t) = 12 15 + 9t + (-1 + 1t) + 4(6 + 4t) = 12 15 + 9t + -1 + 1t + (6 * 4 + 4t * 4) = 12 15 + 9t + -1 + 1t + (24 + 16t) = 12 Reorder the terms: 15 + -1 + 24 + 9t + 1t + 16t = 12 Combine like terms: 15 + -1 = 14 14 + 24 + 9t + 1t + 16t = 12 Combine like terms: 14 + 24 = 38 38 + 9t + 1t + 16t = 12 Combine like terms: 9t + 1t = 10t 38 + 10t + 16t = 12 Combine like terms: 10t + 16t = 26t 38 + 26t = 12 Solving 38 + 26t = 12 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-38' to each side of the equation. 38 + -38 + 26t = 12 + -38 Combine like terms: 38 + -38 = 0 0 + 26t = 12 + -38 26t = 12 + -38 Combine like terms: 12 + -38 = -26 26t = -26 Divide each side by '26'. t = -1 Simplifying t = -1
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