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Simplifying 0.4(2t + 6) + 0.1 = 0.5(2t + -3) Reorder the terms: 0.4(6 + 2t) + 0.1 = 0.5(2t + -3) (6 * 0.4 + 2t * 0.4) + 0.1 = 0.5(2t + -3) (2.4 + 0.8t) + 0.1 = 0.5(2t + -3) Reorder the terms: 2.4 + 0.1 + 0.8t = 0.5(2t + -3) Combine like terms: 2.4 + 0.1 = 2.5 2.5 + 0.8t = 0.5(2t + -3) Reorder the terms: 2.5 + 0.8t = 0.5(-3 + 2t) 2.5 + 0.8t = (-3 * 0.5 + 2t * 0.5) 2.5 + 0.8t = (-1.5 + 1t) Solving 2.5 + 0.8t = -1.5 + 1t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1t' to each side of the equation. 2.5 + 0.8t + -1t = -1.5 + 1t + -1t Combine like terms: 0.8t + -1t = -0.2t 2.5 + -0.2t = -1.5 + 1t + -1t Combine like terms: 1t + -1t = 0 2.5 + -0.2t = -1.5 + 0 2.5 + -0.2t = -1.5 Add '-2.5' to each side of the equation. 2.5 + -2.5 + -0.2t = -1.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -0.2t = -1.5 + -2.5 -0.2t = -1.5 + -2.5 Combine like terms: -1.5 + -2.5 = -4 -0.2t = -4 Divide each side by '-0.2'. t = 20 Simplifying t = 20
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