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Simplifying -0.02[0.4 + -0.1(2 + 3t)] = 0.004t + 0.005 -0.02[0.4 + (2 * -0.1 + 3t * -0.1)] = 0.004t + 0.005 -0.02[0.4 + (-0.2 + -0.3t)] = 0.004t + 0.005 Combine like terms: 0.4 + -0.2 = 0.2 -0.02[0.2 + -0.3t] = 0.004t + 0.005 [0.2 * -0.02 + -0.3t * -0.02] = 0.004t + 0.005 [-0.004 + 0.006t] = 0.004t + 0.005 Reorder the terms: -0.004 + 0.006t = 0.005 + 0.004t Solving -0.004 + 0.006t = 0.005 + 0.004t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.004t' to each side of the equation. -0.004 + 0.006t + -0.004t = 0.005 + 0.004t + -0.004t Combine like terms: 0.006t + -0.004t = 0.002t -0.004 + 0.002t = 0.005 + 0.004t + -0.004t Combine like terms: 0.004t + -0.004t = 0.000 -0.004 + 0.002t = 0.005 + 0.000 -0.004 + 0.002t = 0.005 Add '0.004' to each side of the equation. -0.004 + 0.004 + 0.002t = 0.005 + 0.004 Combine like terms: -0.004 + 0.004 = 0.000 0.000 + 0.002t = 0.005 + 0.004 0.002t = 0.005 + 0.004 Combine like terms: 0.005 + 0.004 = 0.009 0.002t = 0.009 Divide each side by '0.002'. t = 4.5 Simplifying t = 4.5
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