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Simplifying 2(t + -2) + 3(2t + 2) = -5(2 + -1t) Reorder the terms: 2(-2 + t) + 3(2t + 2) = -5(2 + -1t) (-2 * 2 + t * 2) + 3(2t + 2) = -5(2 + -1t) (-4 + 2t) + 3(2t + 2) = -5(2 + -1t) Reorder the terms: -4 + 2t + 3(2 + 2t) = -5(2 + -1t) -4 + 2t + (2 * 3 + 2t * 3) = -5(2 + -1t) -4 + 2t + (6 + 6t) = -5(2 + -1t) Reorder the terms: -4 + 6 + 2t + 6t = -5(2 + -1t) Combine like terms: -4 + 6 = 2 2 + 2t + 6t = -5(2 + -1t) Combine like terms: 2t + 6t = 8t 2 + 8t = -5(2 + -1t) 2 + 8t = (2 * -5 + -1t * -5) 2 + 8t = (-10 + 5t) Solving 2 + 8t = -10 + 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. 2 + 8t + -5t = -10 + 5t + -5t Combine like terms: 8t + -5t = 3t 2 + 3t = -10 + 5t + -5t Combine like terms: 5t + -5t = 0 2 + 3t = -10 + 0 2 + 3t = -10 Add '-2' to each side of the equation. 2 + -2 + 3t = -10 + -2 Combine like terms: 2 + -2 = 0 0 + 3t = -10 + -2 3t = -10 + -2 Combine like terms: -10 + -2 = -12 3t = -12 Divide each side by '3'. t = -4 Simplifying t = -4
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