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Simplifying 7(t + -2) + -1(-3t + 1) = -3(1 + -3t) Reorder the terms: 7(-2 + t) + -1(-3t + 1) = -3(1 + -3t) (-2 * 7 + t * 7) + -1(-3t + 1) = -3(1 + -3t) (-14 + 7t) + -1(-3t + 1) = -3(1 + -3t) Reorder the terms: -14 + 7t + -1(1 + -3t) = -3(1 + -3t) -14 + 7t + (1 * -1 + -3t * -1) = -3(1 + -3t) -14 + 7t + (-1 + 3t) = -3(1 + -3t) Reorder the terms: -14 + -1 + 7t + 3t = -3(1 + -3t) Combine like terms: -14 + -1 = -15 -15 + 7t + 3t = -3(1 + -3t) Combine like terms: 7t + 3t = 10t -15 + 10t = -3(1 + -3t) -15 + 10t = (1 * -3 + -3t * -3) -15 + 10t = (-3 + 9t) Solving -15 + 10t = -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. -15 + 10t + -9t = -3 + 9t + -9t Combine like terms: 10t + -9t = 1t -15 + 1t = -3 + 9t + -9t Combine like terms: 9t + -9t = 0 -15 + 1t = -3 + 0 -15 + 1t = -3 Add '15' to each side of the equation. -15 + 15 + 1t = -3 + 15 Combine like terms: -15 + 15 = 0 0 + 1t = -3 + 15 1t = -3 + 15 Combine like terms: -3 + 15 = 12 1t = 12 Divide each side by '1'. t = 12 Simplifying t = 12
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