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Simplifying 8 + -1(4 + -12t) + 2 = 3t + 2(7 + -3t) 8 + (4 * -1 + -12t * -1) + 2 = 3t + 2(7 + -3t) 8 + (-4 + 12t) + 2 = 3t + 2(7 + -3t) Reorder the terms: 8 + -4 + 2 + 12t = 3t + 2(7 + -3t) Combine like terms: 8 + -4 = 4 4 + 2 + 12t = 3t + 2(7 + -3t) Combine like terms: 4 + 2 = 6 6 + 12t = 3t + 2(7 + -3t) 6 + 12t = 3t + (7 * 2 + -3t * 2) 6 + 12t = 3t + (14 + -6t) Reorder the terms: 6 + 12t = 14 + 3t + -6t Combine like terms: 3t + -6t = -3t 6 + 12t = 14 + -3t Solving 6 + 12t = 14 + -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. 6 + 12t + 3t = 14 + -3t + 3t Combine like terms: 12t + 3t = 15t 6 + 15t = 14 + -3t + 3t Combine like terms: -3t + 3t = 0 6 + 15t = 14 + 0 6 + 15t = 14 Add '-6' to each side of the equation. 6 + -6 + 15t = 14 + -6 Combine like terms: 6 + -6 = 0 0 + 15t = 14 + -6 15t = 14 + -6 Combine like terms: 14 + -6 = 8 15t = 8 Divide each side by '15'. t = 0.5333333333 Simplifying t = 0.5333333333
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