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Simplifying 3(t + 6) + 3(-4t + -9) = -10(t + 2) + -3 Reorder the terms: 3(6 + t) + 3(-4t + -9) = -10(t + 2) + -3 (6 * 3 + t * 3) + 3(-4t + -9) = -10(t + 2) + -3 (18 + 3t) + 3(-4t + -9) = -10(t + 2) + -3 Reorder the terms: 18 + 3t + 3(-9 + -4t) = -10(t + 2) + -3 18 + 3t + (-9 * 3 + -4t * 3) = -10(t + 2) + -3 18 + 3t + (-27 + -12t) = -10(t + 2) + -3 Reorder the terms: 18 + -27 + 3t + -12t = -10(t + 2) + -3 Combine like terms: 18 + -27 = -9 -9 + 3t + -12t = -10(t + 2) + -3 Combine like terms: 3t + -12t = -9t -9 + -9t = -10(t + 2) + -3 Reorder the terms: -9 + -9t = -10(2 + t) + -3 -9 + -9t = (2 * -10 + t * -10) + -3 -9 + -9t = (-20 + -10t) + -3 Reorder the terms: -9 + -9t = -20 + -3 + -10t Combine like terms: -20 + -3 = -23 -9 + -9t = -23 + -10t Solving -9 + -9t = -23 + -10t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10t' to each side of the equation. -9 + -9t + 10t = -23 + -10t + 10t Combine like terms: -9t + 10t = 1t -9 + 1t = -23 + -10t + 10t Combine like terms: -10t + 10t = 0 -9 + 1t = -23 + 0 -9 + 1t = -23 Add '9' to each side of the equation. -9 + 9 + 1t = -23 + 9 Combine like terms: -9 + 9 = 0 0 + 1t = -23 + 9 1t = -23 + 9 Combine like terms: -23 + 9 = -14 1t = -14 Divide each side by '1'. t = -14 Simplifying t = -14
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