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Simplifying 2(2t + 9) + -3t = 2 + -6(3t + 10) Reorder the terms: 2(9 + 2t) + -3t = 2 + -6(3t + 10) (9 * 2 + 2t * 2) + -3t = 2 + -6(3t + 10) (18 + 4t) + -3t = 2 + -6(3t + 10) Combine like terms: 4t + -3t = 1t 18 + 1t = 2 + -6(3t + 10) Reorder the terms: 18 + 1t = 2 + -6(10 + 3t) 18 + 1t = 2 + (10 * -6 + 3t * -6) 18 + 1t = 2 + (-60 + -18t) Combine like terms: 2 + -60 = -58 18 + 1t = -58 + -18t Solving 18 + 1t = -58 + -18t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '18t' to each side of the equation. 18 + 1t + 18t = -58 + -18t + 18t Combine like terms: 1t + 18t = 19t 18 + 19t = -58 + -18t + 18t Combine like terms: -18t + 18t = 0 18 + 19t = -58 + 0 18 + 19t = -58 Add '-18' to each side of the equation. 18 + -18 + 19t = -58 + -18 Combine like terms: 18 + -18 = 0 0 + 19t = -58 + -18 19t = -58 + -18 Combine like terms: -58 + -18 = -76 19t = -76 Divide each side by '19'. t = -4 Simplifying t = -4
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