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Simplifying t + -1(2t + -5) + -5(1 + -5t) = 2(3 + 4t) + -3(t + -4) Reorder the terms: t + -1(-5 + 2t) + -5(1 + -5t) = 2(3 + 4t) + -3(t + -4) t + (-5 * -1 + 2t * -1) + -5(1 + -5t) = 2(3 + 4t) + -3(t + -4) t + (5 + -2t) + -5(1 + -5t) = 2(3 + 4t) + -3(t + -4) t + 5 + -2t + (1 * -5 + -5t * -5) = 2(3 + 4t) + -3(t + -4) t + 5 + -2t + (-5 + 25t) = 2(3 + 4t) + -3(t + -4) Reorder the terms: 5 + -5 + t + -2t + 25t = 2(3 + 4t) + -3(t + -4) Combine like terms: 5 + -5 = 0 0 + t + -2t + 25t = 2(3 + 4t) + -3(t + -4) t + -2t + 25t = 2(3 + 4t) + -3(t + -4) Combine like terms: t + -2t = -1t -1t + 25t = 2(3 + 4t) + -3(t + -4) Combine like terms: -1t + 25t = 24t 24t = 2(3 + 4t) + -3(t + -4) 24t = (3 * 2 + 4t * 2) + -3(t + -4) 24t = (6 + 8t) + -3(t + -4) Reorder the terms: 24t = 6 + 8t + -3(-4 + t) 24t = 6 + 8t + (-4 * -3 + t * -3) 24t = 6 + 8t + (12 + -3t) Reorder the terms: 24t = 6 + 12 + 8t + -3t Combine like terms: 6 + 12 = 18 24t = 18 + 8t + -3t Combine like terms: 8t + -3t = 5t 24t = 18 + 5t Solving 24t = 18 + 5t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5t' to each side of the equation. 24t + -5t = 18 + 5t + -5t Combine like terms: 24t + -5t = 19t 19t = 18 + 5t + -5t Combine like terms: 5t + -5t = 0 19t = 18 + 0 19t = 18 Divide each side by '19'. t = 0.9473684211 Simplifying t = 0.9473684211
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