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Simplifying 0.7(6t + -3) = 0.42(t + -3) + 1.05 Reorder the terms: 0.7(-3 + 6t) = 0.42(t + -3) + 1.05 (-3 * 0.7 + 6t * 0.7) = 0.42(t + -3) + 1.05 (-2.1 + 4.2t) = 0.42(t + -3) + 1.05 Reorder the terms: -2.1 + 4.2t = 0.42(-3 + t) + 1.05 -2.1 + 4.2t = (-3 * 0.42 + t * 0.42) + 1.05 -2.1 + 4.2t = (-1.26 + 0.42t) + 1.05 Reorder the terms: -2.1 + 4.2t = -1.26 + 1.05 + 0.42t Combine like terms: -1.26 + 1.05 = -0.21 -2.1 + 4.2t = -0.21 + 0.42t Solving -2.1 + 4.2t = -0.21 + 0.42t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.42t' to each side of the equation. -2.1 + 4.2t + -0.42t = -0.21 + 0.42t + -0.42t Combine like terms: 4.2t + -0.42t = 3.78t -2.1 + 3.78t = -0.21 + 0.42t + -0.42t Combine like terms: 0.42t + -0.42t = 0.00 -2.1 + 3.78t = -0.21 + 0.00 -2.1 + 3.78t = -0.21 Add '2.1' to each side of the equation. -2.1 + 2.1 + 3.78t = -0.21 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + 3.78t = -0.21 + 2.1 3.78t = -0.21 + 2.1 Combine like terms: -0.21 + 2.1 = 1.89 3.78t = 1.89 Divide each side by '3.78'. t = 0.5 Simplifying t = 0.5
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