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Simplifying 5.2t + 14.6 + -10.1t = 12.8 + -3.5t + -0.6 Reorder the terms: 14.6 + 5.2t + -10.1t = 12.8 + -3.5t + -0.6 Combine like terms: 5.2t + -10.1t = -4.9t 14.6 + -4.9t = 12.8 + -3.5t + -0.6 Reorder the terms: 14.6 + -4.9t = 12.8 + -0.6 + -3.5t Combine like terms: 12.8 + -0.6 = 12.2 14.6 + -4.9t = 12.2 + -3.5t Solving 14.6 + -4.9t = 12.2 + -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 + -4.9t + 3.5t = 12.2 + -3.5t + 3.5t Combine like terms: -4.9t + 3.5t = -1.4t 14.6 + -1.4t = 12.2 + -3.5t + 3.5t Combine like terms: -3.5t + 3.5t = 0.0 14.6 + -1.4t = 12.2 + 0.0 14.6 + -1.4t = 12.2 Add '-14.6' to each side of the equation. 14.6 + -14.6 + -1.4t = 12.2 + -14.6 Combine like terms: 14.6 + -14.6 = 0.0 0.0 + -1.4t = 12.2 + -14.6 -1.4t = 12.2 + -14.6 Combine like terms: 12.2 + -14.6 = -2.4 -1.4t = -2.4 Divide each side by '-1.4'. t = 1.714285714 Simplifying t = 1.714285714
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