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Simplifying (7t + -2) + -1(-3t + 1) = -2(1 + -3t) Reorder the terms: (-2 + 7t) + -1(-3t + 1) = -2(1 + -3t) Remove parenthesis around (-2 + 7t) -2 + 7t + -1(-3t + 1) = -2(1 + -3t) Reorder the terms: -2 + 7t + -1(1 + -3t) = -2(1 + -3t) -2 + 7t + (1 * -1 + -3t * -1) = -2(1 + -3t) -2 + 7t + (-1 + 3t) = -2(1 + -3t) Reorder the terms: -2 + -1 + 7t + 3t = -2(1 + -3t) Combine like terms: -2 + -1 = -3 -3 + 7t + 3t = -2(1 + -3t) Combine like terms: 7t + 3t = 10t -3 + 10t = -2(1 + -3t) -3 + 10t = (1 * -2 + -3t * -2) -3 + 10t = (-2 + 6t) Solving -3 + 10t = -2 + 6t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6t' to each side of the equation. -3 + 10t + -6t = -2 + 6t + -6t Combine like terms: 10t + -6t = 4t -3 + 4t = -2 + 6t + -6t Combine like terms: 6t + -6t = 0 -3 + 4t = -2 + 0 -3 + 4t = -2 Add '3' to each side of the equation. -3 + 3 + 4t = -2 + 3 Combine like terms: -3 + 3 = 0 0 + 4t = -2 + 3 4t = -2 + 3 Combine like terms: -2 + 3 = 1 4t = 1 Divide each side by '4'. t = 0.25 Simplifying t = 0.25
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