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Simplifying 9(t + 3) + 2(3t + 5) = 14(t + 2) + 2 Reorder the terms: 9(3 + t) + 2(3t + 5) = 14(t + 2) + 2 (3 * 9 + t * 9) + 2(3t + 5) = 14(t + 2) + 2 (27 + 9t) + 2(3t + 5) = 14(t + 2) + 2 Reorder the terms: 27 + 9t + 2(5 + 3t) = 14(t + 2) + 2 27 + 9t + (5 * 2 + 3t * 2) = 14(t + 2) + 2 27 + 9t + (10 + 6t) = 14(t + 2) + 2 Reorder the terms: 27 + 10 + 9t + 6t = 14(t + 2) + 2 Combine like terms: 27 + 10 = 37 37 + 9t + 6t = 14(t + 2) + 2 Combine like terms: 9t + 6t = 15t 37 + 15t = 14(t + 2) + 2 Reorder the terms: 37 + 15t = 14(2 + t) + 2 37 + 15t = (2 * 14 + t * 14) + 2 37 + 15t = (28 + 14t) + 2 Reorder the terms: 37 + 15t = 28 + 2 + 14t Combine like terms: 28 + 2 = 30 37 + 15t = 30 + 14t Solving 37 + 15t = 30 + 14t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-14t' to each side of the equation. 37 + 15t + -14t = 30 + 14t + -14t Combine like terms: 15t + -14t = 1t 37 + 1t = 30 + 14t + -14t Combine like terms: 14t + -14t = 0 37 + 1t = 30 + 0 37 + 1t = 30 Add '-37' to each side of the equation. 37 + -37 + 1t = 30 + -37 Combine like terms: 37 + -37 = 0 0 + 1t = 30 + -37 1t = 30 + -37 Combine like terms: 30 + -37 = -7 1t = -7 Divide each side by '1'. t = -7 Simplifying t = -7
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