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Simplifying 5.4t + 14.6 + -10.1t = 12.8t + -3.5t + -0.6 Reorder the terms: 14.6 + 5.4t + -10.1t = 12.8t + -3.5t + -0.6 Combine like terms: 5.4t + -10.1t = -4.7t 14.6 + -4.7t = 12.8t + -3.5t + -0.6 Reorder the terms: 14.6 + -4.7t = -0.6 + 12.8t + -3.5t Combine like terms: 12.8t + -3.5t = 9.3t 14.6 + -4.7t = -0.6 + 9.3t Solving 14.6 + -4.7t = -0.6 + 9.3t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9.3t' to each side of the equation. 14.6 + -4.7t + -9.3t = -0.6 + 9.3t + -9.3t Combine like terms: -4.7t + -9.3t = -14t 14.6 + -14t = -0.6 + 9.3t + -9.3t Combine like terms: 9.3t + -9.3t = 0.0 14.6 + -14t = -0.6 + 0.0 14.6 + -14t = -0.6 Add '-14.6' to each side of the equation. 14.6 + -14.6 + -14t = -0.6 + -14.6 Combine like terms: 14.6 + -14.6 = 0.0 0.0 + -14t = -0.6 + -14.6 -14t = -0.6 + -14.6 Combine like terms: -0.6 + -14.6 = -15.2 -14t = -15.2 Divide each side by '-14'. t = 1.085714286 Simplifying t = 1.085714286
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