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Simplifying 2(t + -10) + -3(3t + -5) = 7 + -5(5t + 1) Reorder the terms: 2(-10 + t) + -3(3t + -5) = 7 + -5(5t + 1) (-10 * 2 + t * 2) + -3(3t + -5) = 7 + -5(5t + 1) (-20 + 2t) + -3(3t + -5) = 7 + -5(5t + 1) Reorder the terms: -20 + 2t + -3(-5 + 3t) = 7 + -5(5t + 1) -20 + 2t + (-5 * -3 + 3t * -3) = 7 + -5(5t + 1) -20 + 2t + (15 + -9t) = 7 + -5(5t + 1) Reorder the terms: -20 + 15 + 2t + -9t = 7 + -5(5t + 1) Combine like terms: -20 + 15 = -5 -5 + 2t + -9t = 7 + -5(5t + 1) Combine like terms: 2t + -9t = -7t -5 + -7t = 7 + -5(5t + 1) Reorder the terms: -5 + -7t = 7 + -5(1 + 5t) -5 + -7t = 7 + (1 * -5 + 5t * -5) -5 + -7t = 7 + (-5 + -25t) Combine like terms: 7 + -5 = 2 -5 + -7t = 2 + -25t Solving -5 + -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. -5 + -7t + 25t = 2 + -25t + 25t Combine like terms: -7t + 25t = 18t -5 + 18t = 2 + -25t + 25t Combine like terms: -25t + 25t = 0 -5 + 18t = 2 + 0 -5 + 18t = 2 Add '5' to each side of the equation. -5 + 5 + 18t = 2 + 5 Combine like terms: -5 + 5 = 0 0 + 18t = 2 + 5 18t = 2 + 5 Combine like terms: 2 + 5 = 7 18t = 7 Divide each side by '18'. t = 0.3888888889 Simplifying t = 0.3888888889
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