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Simplifying 3(t + -9) + 2(t + 6) = -3(t + 5) + -3 Reorder the terms: 3(-9 + t) + 2(t + 6) = -3(t + 5) + -3 (-9 * 3 + t * 3) + 2(t + 6) = -3(t + 5) + -3 (-27 + 3t) + 2(t + 6) = -3(t + 5) + -3 Reorder the terms: -27 + 3t + 2(6 + t) = -3(t + 5) + -3 -27 + 3t + (6 * 2 + t * 2) = -3(t + 5) + -3 -27 + 3t + (12 + 2t) = -3(t + 5) + -3 Reorder the terms: -27 + 12 + 3t + 2t = -3(t + 5) + -3 Combine like terms: -27 + 12 = -15 -15 + 3t + 2t = -3(t + 5) + -3 Combine like terms: 3t + 2t = 5t -15 + 5t = -3(t + 5) + -3 Reorder the terms: -15 + 5t = -3(5 + t) + -3 -15 + 5t = (5 * -3 + t * -3) + -3 -15 + 5t = (-15 + -3t) + -3 Reorder the terms: -15 + 5t = -15 + -3 + -3t Combine like terms: -15 + -3 = -18 -15 + 5t = -18 + -3t Solving -15 + 5t = -18 + -3t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3t' to each side of the equation. -15 + 5t + 3t = -18 + -3t + 3t Combine like terms: 5t + 3t = 8t -15 + 8t = -18 + -3t + 3t Combine like terms: -3t + 3t = 0 -15 + 8t = -18 + 0 -15 + 8t = -18 Add '15' to each side of the equation. -15 + 15 + 8t = -18 + 15 Combine like terms: -15 + 15 = 0 0 + 8t = -18 + 15 8t = -18 + 15 Combine like terms: -18 + 15 = -3 8t = -3 Divide each side by '8'. t = -0.375 Simplifying t = -0.375
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