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