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Simplifying t + (2t + 5) + -5(1 + -2t) = 2(3 + 4t) + -3(t + -4) Reorder the terms: t + (5 + 2t) + -5(1 + -2t) = 2(3 + 4t) + -3(t + -4) Remove parenthesis around (5 + 2t) t + 5 + 2t + -5(1 + -2t) = 2(3 + 4t) + -3(t + -4) t + 5 + 2t + (1 * -5 + -2t * -5) = 2(3 + 4t) + -3(t + -4) t + 5 + 2t + (-5 + 10t) = 2(3 + 4t) + -3(t + -4) Reorder the terms: 5 + -5 + t + 2t + 10t = 2(3 + 4t) + -3(t + -4) Combine like terms: 5 + -5 = 0 0 + t + 2t + 10t = 2(3 + 4t) + -3(t + -4) t + 2t + 10t = 2(3 + 4t) + -3(t + -4) Combine like terms: t + 2t = 3t 3t + 10t = 2(3 + 4t) + -3(t + -4) Combine like terms: 3t + 10t = 13t 13t = 2(3 + 4t) + -3(t + -4) 13t = (3 * 2 + 4t * 2) + -3(t + -4) 13t = (6 + 8t) + -3(t + -4) Reorder the terms: 13t = 6 + 8t + -3(-4 + t) 13t = 6 + 8t + (-4 * -3 + t * -3) 13t = 6 + 8t + (12 + -3t) Reorder the terms: 13t = 6 + 12 + 8t + -3t Combine like terms: 6 + 12 = 18 13t = 18 + 8t + -3t Combine like terms: 8t + -3t = 5t 13t = 18 + 5t Solving 13t = 18 + 5t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5t' to each side of the equation. 13t + -5t = 18 + 5t + -5t Combine like terms: 13t + -5t = 8t 8t = 18 + 5t + -5t Combine like terms: 5t + -5t = 0 8t = 18 + 0 8t = 18 Divide each side by '8'. t = 2.25 Simplifying t = 2.25
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