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Simplifying 5.4t + 14.6 + -10.1t = 12.8 + -3.5t + -0.8 Reorder the terms: 14.6 + 5.4t + -10.1t = 12.8 + -3.5t + -0.8 Combine like terms: 5.4t + -10.1t = -4.7t 14.6 + -4.7t = 12.8 + -3.5t + -0.8 Reorder the terms: 14.6 + -4.7t = 12.8 + -0.8 + -3.5t Combine like terms: 12.8 + -0.8 = 12 14.6 + -4.7t = 12 + -3.5t Solving 14.6 + -4.7t = 12 + -3.5t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5t' to each side of the equation. 14.6 + -4.7t + 3.5t = 12 + -3.5t + 3.5t Combine like terms: -4.7t + 3.5t = -1.2t 14.6 + -1.2t = 12 + -3.5t + 3.5t Combine like terms: -3.5t + 3.5t = 0.0 14.6 + -1.2t = 12 + 0.0 14.6 + -1.2t = 12 Add '-14.6' to each side of the equation. 14.6 + -14.6 + -1.2t = 12 + -14.6 Combine like terms: 14.6 + -14.6 = 0.0 0.0 + -1.2t = 12 + -14.6 -1.2t = 12 + -14.6 Combine like terms: 12 + -14.6 = -2.6 -1.2t = -2.6 Divide each side by '-1.2'. t = 2.166666667 Simplifying t = 2.166666667
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