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Simplifying 2(t + -1) + 3(t + 2) = -5(7 + -3t) Reorder the terms: 2(-1 + t) + 3(t + 2) = -5(7 + -3t) (-1 * 2 + t * 2) + 3(t + 2) = -5(7 + -3t) (-2 + 2t) + 3(t + 2) = -5(7 + -3t) Reorder the terms: -2 + 2t + 3(2 + t) = -5(7 + -3t) -2 + 2t + (2 * 3 + t * 3) = -5(7 + -3t) -2 + 2t + (6 + 3t) = -5(7 + -3t) Reorder the terms: -2 + 6 + 2t + 3t = -5(7 + -3t) Combine like terms: -2 + 6 = 4 4 + 2t + 3t = -5(7 + -3t) Combine like terms: 2t + 3t = 5t 4 + 5t = -5(7 + -3t) 4 + 5t = (7 * -5 + -3t * -5) 4 + 5t = (-35 + 15t) Solving 4 + 5t = -35 + 15t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15t' to each side of the equation. 4 + 5t + -15t = -35 + 15t + -15t Combine like terms: 5t + -15t = -10t 4 + -10t = -35 + 15t + -15t Combine like terms: 15t + -15t = 0 4 + -10t = -35 + 0 4 + -10t = -35 Add '-4' to each side of the equation. 4 + -4 + -10t = -35 + -4 Combine like terms: 4 + -4 = 0 0 + -10t = -35 + -4 -10t = -35 + -4 Combine like terms: -35 + -4 = -39 -10t = -39 Divide each side by '-10'. t = 3.9 Simplifying t = 3.9
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