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Simplifying 2(t + -1) + -3(3t + -2) = 3 + -5(4t + 1) Reorder the terms: 2(-1 + t) + -3(3t + -2) = 3 + -5(4t + 1) (-1 * 2 + t * 2) + -3(3t + -2) = 3 + -5(4t + 1) (-2 + 2t) + -3(3t + -2) = 3 + -5(4t + 1) Reorder the terms: -2 + 2t + -3(-2 + 3t) = 3 + -5(4t + 1) -2 + 2t + (-2 * -3 + 3t * -3) = 3 + -5(4t + 1) -2 + 2t + (6 + -9t) = 3 + -5(4t + 1) Reorder the terms: -2 + 6 + 2t + -9t = 3 + -5(4t + 1) Combine like terms: -2 + 6 = 4 4 + 2t + -9t = 3 + -5(4t + 1) Combine like terms: 2t + -9t = -7t 4 + -7t = 3 + -5(4t + 1) Reorder the terms: 4 + -7t = 3 + -5(1 + 4t) 4 + -7t = 3 + (1 * -5 + 4t * -5) 4 + -7t = 3 + (-5 + -20t) Combine like terms: 3 + -5 = -2 4 + -7t = -2 + -20t Solving 4 + -7t = -2 + -20t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20t' to each side of the equation. 4 + -7t + 20t = -2 + -20t + 20t Combine like terms: -7t + 20t = 13t 4 + 13t = -2 + -20t + 20t Combine like terms: -20t + 20t = 0 4 + 13t = -2 + 0 4 + 13t = -2 Add '-4' to each side of the equation. 4 + -4 + 13t = -2 + -4 Combine like terms: 4 + -4 = 0 0 + 13t = -2 + -4 13t = -2 + -4 Combine like terms: -2 + -4 = -6 13t = -6 Divide each side by '13'. t = -0.4615384615 Simplifying t = -0.4615384615
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