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Simplifying 7(t + -2) + -1(-3t + 1) = -3(1 + -1t) Reorder the terms: 7(-2 + t) + -1(-3t + 1) = -3(1 + -1t) (-2 * 7 + t * 7) + -1(-3t + 1) = -3(1 + -1t) (-14 + 7t) + -1(-3t + 1) = -3(1 + -1t) Reorder the terms: -14 + 7t + -1(1 + -3t) = -3(1 + -1t) -14 + 7t + (1 * -1 + -3t * -1) = -3(1 + -1t) -14 + 7t + (-1 + 3t) = -3(1 + -1t) Reorder the terms: -14 + -1 + 7t + 3t = -3(1 + -1t) Combine like terms: -14 + -1 = -15 -15 + 7t + 3t = -3(1 + -1t) Combine like terms: 7t + 3t = 10t -15 + 10t = -3(1 + -1t) -15 + 10t = (1 * -3 + -1t * -3) -15 + 10t = (-3 + 3t) Solving -15 + 10t = -3 + 3t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3t' to each side of the equation. -15 + 10t + -3t = -3 + 3t + -3t Combine like terms: 10t + -3t = 7t -15 + 7t = -3 + 3t + -3t Combine like terms: 3t + -3t = 0 -15 + 7t = -3 + 0 -15 + 7t = -3 Add '15' to each side of the equation. -15 + 15 + 7t = -3 + 15 Combine like terms: -15 + 15 = 0 0 + 7t = -3 + 15 7t = -3 + 15 Combine like terms: -3 + 15 = 12 7t = 12 Divide each side by '7'. t = 1.714285714 Simplifying t = 1.714285714
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