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Simplifying 7t + -1(30 + -2t) = 8(3t + 1) 7t + (30 * -1 + -2t * -1) = 8(3t + 1) 7t + (-30 + 2t) = 8(3t + 1) Reorder the terms: -30 + 7t + 2t = 8(3t + 1) Combine like terms: 7t + 2t = 9t -30 + 9t = 8(3t + 1) Reorder the terms: -30 + 9t = 8(1 + 3t) -30 + 9t = (1 * 8 + 3t * 8) -30 + 9t = (8 + 24t) Solving -30 + 9t = 8 + 24t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-24t' to each side of the equation. -30 + 9t + -24t = 8 + 24t + -24t Combine like terms: 9t + -24t = -15t -30 + -15t = 8 + 24t + -24t Combine like terms: 24t + -24t = 0 -30 + -15t = 8 + 0 -30 + -15t = 8 Add '30' to each side of the equation. -30 + 30 + -15t = 8 + 30 Combine like terms: -30 + 30 = 0 0 + -15t = 8 + 30 -15t = 8 + 30 Combine like terms: 8 + 30 = 38 -15t = 38 Divide each side by '-15'. t = -2.533333333 Simplifying t = -2.533333333
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