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Simplifying 2(t + -1) + -3(3t + -5) = 7 + -5(5t + 1) Reorder the terms: 2(-1 + t) + -3(3t + -5) = 7 + -5(5t + 1) (-1 * 2 + t * 2) + -3(3t + -5) = 7 + -5(5t + 1) (-2 + 2t) + -3(3t + -5) = 7 + -5(5t + 1) Reorder the terms: -2 + 2t + -3(-5 + 3t) = 7 + -5(5t + 1) -2 + 2t + (-5 * -3 + 3t * -3) = 7 + -5(5t + 1) -2 + 2t + (15 + -9t) = 7 + -5(5t + 1) Reorder the terms: -2 + 15 + 2t + -9t = 7 + -5(5t + 1) Combine like terms: -2 + 15 = 13 13 + 2t + -9t = 7 + -5(5t + 1) Combine like terms: 2t + -9t = -7t 13 + -7t = 7 + -5(5t + 1) Reorder the terms: 13 + -7t = 7 + -5(1 + 5t) 13 + -7t = 7 + (1 * -5 + 5t * -5) 13 + -7t = 7 + (-5 + -25t) Combine like terms: 7 + -5 = 2 13 + -7t = 2 + -25t Solving 13 + -7t = 2 + -25t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '25t' to each side of the equation. 13 + -7t + 25t = 2 + -25t + 25t Combine like terms: -7t + 25t = 18t 13 + 18t = 2 + -25t + 25t Combine like terms: -25t + 25t = 0 13 + 18t = 2 + 0 13 + 18t = 2 Add '-13' to each side of the equation. 13 + -13 + 18t = 2 + -13 Combine like terms: 13 + -13 = 0 0 + 18t = 2 + -13 18t = 2 + -13 Combine like terms: 2 + -13 = -11 18t = -11 Divide each side by '18'. t = -0.6111111111 Simplifying t = -0.6111111111
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