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Simplifying 3[6 + -1(4t + 9)] + -3 = 4(3 + -1t) Reorder the terms: 3[6 + -1(9 + 4t)] + -3 = 4(3 + -1t) 3[6 + (9 * -1 + 4t * -1)] + -3 = 4(3 + -1t) 3[6 + (-9 + -4t)] + -3 = 4(3 + -1t) Combine like terms: 6 + -9 = -3 3[-3 + -4t] + -3 = 4(3 + -1t) [-3 * 3 + -4t * 3] + -3 = 4(3 + -1t) [-9 + -12t] + -3 = 4(3 + -1t) Reorder the terms: -9 + -3 + -12t = 4(3 + -1t) Combine like terms: -9 + -3 = -12 -12 + -12t = 4(3 + -1t) -12 + -12t = (3 * 4 + -1t * 4) -12 + -12t = (12 + -4t) Solving -12 + -12t = 12 + -4t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4t' to each side of the equation. -12 + -12t + 4t = 12 + -4t + 4t Combine like terms: -12t + 4t = -8t -12 + -8t = 12 + -4t + 4t Combine like terms: -4t + 4t = 0 -12 + -8t = 12 + 0 -12 + -8t = 12 Add '12' to each side of the equation. -12 + 12 + -8t = 12 + 12 Combine like terms: -12 + 12 = 0 0 + -8t = 12 + 12 -8t = 12 + 12 Combine like terms: 12 + 12 = 24 -8t = 24 Divide each side by '-8'. t = -3 Simplifying t = -3
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