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Simplifying T + -1(2t + 5) + -5(1 + -2t) = 2(3 + 4t) + -1(t + -4) Reorder the terms: T + -1(5 + 2t) + -5(1 + -2t) = 2(3 + 4t) + -1(t + -4) T + (5 * -1 + 2t * -1) + -5(1 + -2t) = 2(3 + 4t) + -1(t + -4) T + (-5 + -2t) + -5(1 + -2t) = 2(3 + 4t) + -1(t + -4) T + -5 + -2t + (1 * -5 + -2t * -5) = 2(3 + 4t) + -1(t + -4) T + -5 + -2t + (-5 + 10t) = 2(3 + 4t) + -1(t + -4) Reorder the terms: -5 + -5 + T + -2t + 10t = 2(3 + 4t) + -1(t + -4) Combine like terms: -5 + -5 = -10 -10 + T + -2t + 10t = 2(3 + 4t) + -1(t + -4) Combine like terms: -2t + 10t = 8t -10 + T + 8t = 2(3 + 4t) + -1(t + -4) -10 + T + 8t = (3 * 2 + 4t * 2) + -1(t + -4) -10 + T + 8t = (6 + 8t) + -1(t + -4) Reorder the terms: -10 + T + 8t = 6 + 8t + -1(-4 + t) -10 + T + 8t = 6 + 8t + (-4 * -1 + t * -1) -10 + T + 8t = 6 + 8t + (4 + -1t) Reorder the terms: -10 + T + 8t = 6 + 4 + 8t + -1t Combine like terms: 6 + 4 = 10 -10 + T + 8t = 10 + 8t + -1t Combine like terms: 8t + -1t = 7t -10 + T + 8t = 10 + 7t Solving -10 + T + 8t = 10 + 7t Solving for variable 'T'. Move all terms containing T to the left, all other terms to the right. Add '10' to each side of the equation. -10 + T + 10 + 8t = 10 + 10 + 7t Reorder the terms: -10 + 10 + T + 8t = 10 + 10 + 7t Combine like terms: -10 + 10 = 0 0 + T + 8t = 10 + 10 + 7t T + 8t = 10 + 10 + 7t Combine like terms: 10 + 10 = 20 T + 8t = 20 + 7t Add '-8t' to each side of the equation. T + 8t + -8t = 20 + 7t + -8t Combine like terms: 8t + -8t = 0 T + 0 = 20 + 7t + -8t T = 20 + 7t + -8t Combine like terms: 7t + -8t = -1t T = 20 + -1t Simplifying T = 20 + -1t
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