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Simplifying 2(t + -1) + -3(4t + -1) = 2 + -5(7t + 1) Reorder the terms: 2(-1 + t) + -3(4t + -1) = 2 + -5(7t + 1) (-1 * 2 + t * 2) + -3(4t + -1) = 2 + -5(7t + 1) (-2 + 2t) + -3(4t + -1) = 2 + -5(7t + 1) Reorder the terms: -2 + 2t + -3(-1 + 4t) = 2 + -5(7t + 1) -2 + 2t + (-1 * -3 + 4t * -3) = 2 + -5(7t + 1) -2 + 2t + (3 + -12t) = 2 + -5(7t + 1) Reorder the terms: -2 + 3 + 2t + -12t = 2 + -5(7t + 1) Combine like terms: -2 + 3 = 1 1 + 2t + -12t = 2 + -5(7t + 1) Combine like terms: 2t + -12t = -10t 1 + -10t = 2 + -5(7t + 1) Reorder the terms: 1 + -10t = 2 + -5(1 + 7t) 1 + -10t = 2 + (1 * -5 + 7t * -5) 1 + -10t = 2 + (-5 + -35t) Combine like terms: 2 + -5 = -3 1 + -10t = -3 + -35t Solving 1 + -10t = -3 + -35t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35t' to each side of the equation. 1 + -10t + 35t = -3 + -35t + 35t Combine like terms: -10t + 35t = 25t 1 + 25t = -3 + -35t + 35t Combine like terms: -35t + 35t = 0 1 + 25t = -3 + 0 1 + 25t = -3 Add '-1' to each side of the equation. 1 + -1 + 25t = -3 + -1 Combine like terms: 1 + -1 = 0 0 + 25t = -3 + -1 25t = -3 + -1 Combine like terms: -3 + -1 = -4 25t = -4 Divide each side by '25'. t = -0.16 Simplifying t = -0.16
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