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Simplifying 0.03(3t + -9) = 0.18(t + -4) + 0.45 Reorder the terms: 0.03(-9 + 3t) = 0.18(t + -4) + 0.45 (-9 * 0.03 + 3t * 0.03) = 0.18(t + -4) + 0.45 (-0.27 + 0.09t) = 0.18(t + -4) + 0.45 Reorder the terms: -0.27 + 0.09t = 0.18(-4 + t) + 0.45 -0.27 + 0.09t = (-4 * 0.18 + t * 0.18) + 0.45 -0.27 + 0.09t = (-0.72 + 0.18t) + 0.45 Reorder the terms: -0.27 + 0.09t = -0.72 + 0.45 + 0.18t Combine like terms: -0.72 + 0.45 = -0.27 -0.27 + 0.09t = -0.27 + 0.18t Add '0.27' to each side of the equation. -0.27 + 0.27 + 0.09t = -0.27 + 0.27 + 0.18t Combine like terms: -0.27 + 0.27 = 0.00 0.00 + 0.09t = -0.27 + 0.27 + 0.18t 0.09t = -0.27 + 0.27 + 0.18t Combine like terms: -0.27 + 0.27 = 0.00 0.09t = 0.00 + 0.18t 0.09t = 0.18t Solving 0.09t = 0.18t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.18t' to each side of the equation. 0.09t + -0.18t = 0.18t + -0.18t Combine like terms: 0.09t + -0.18t = -0.09t -0.09t = 0.18t + -0.18t Combine like terms: 0.18t + -0.18t = 0.00 -0.09t = 0.00 Divide each side by '-0.09'. t = 0 Simplifying t = 0
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