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Simplifying 5.4t + 14.6 + -10.1t = 12.8 + -3.8t + -0.6 Reorder the terms: 14.6 + 5.4t + -10.1t = 12.8 + -3.8t + -0.6 Combine like terms: 5.4t + -10.1t = -4.7t 14.6 + -4.7t = 12.8 + -3.8t + -0.6 Reorder the terms: 14.6 + -4.7t = 12.8 + -0.6 + -3.8t Combine like terms: 12.8 + -0.6 = 12.2 14.6 + -4.7t = 12.2 + -3.8t Solving 14.6 + -4.7t = 12.2 + -3.8t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.8t' to each side of the equation. 14.6 + -4.7t + 3.8t = 12.2 + -3.8t + 3.8t Combine like terms: -4.7t + 3.8t = -0.9t 14.6 + -0.9t = 12.2 + -3.8t + 3.8t Combine like terms: -3.8t + 3.8t = 0.0 14.6 + -0.9t = 12.2 + 0.0 14.6 + -0.9t = 12.2 Add '-14.6' to each side of the equation. 14.6 + -14.6 + -0.9t = 12.2 + -14.6 Combine like terms: 14.6 + -14.6 = 0.0 0.0 + -0.9t = 12.2 + -14.6 -0.9t = 12.2 + -14.6 Combine like terms: 12.2 + -14.6 = -2.4 -0.9t = -2.4 Divide each side by '-0.9'. t = 2.666666667 Simplifying t = 2.666666667
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