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