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Simplifying 3(t + 4) + 2(8 + -9t) = -16(t + -3) + -8 Reorder the terms: 3(4 + t) + 2(8 + -9t) = -16(t + -3) + -8 (4 * 3 + t * 3) + 2(8 + -9t) = -16(t + -3) + -8 (12 + 3t) + 2(8 + -9t) = -16(t + -3) + -8 12 + 3t + (8 * 2 + -9t * 2) = -16(t + -3) + -8 12 + 3t + (16 + -18t) = -16(t + -3) + -8 Reorder the terms: 12 + 16 + 3t + -18t = -16(t + -3) + -8 Combine like terms: 12 + 16 = 28 28 + 3t + -18t = -16(t + -3) + -8 Combine like terms: 3t + -18t = -15t 28 + -15t = -16(t + -3) + -8 Reorder the terms: 28 + -15t = -16(-3 + t) + -8 28 + -15t = (-3 * -16 + t * -16) + -8 28 + -15t = (48 + -16t) + -8 Reorder the terms: 28 + -15t = 48 + -8 + -16t Combine like terms: 48 + -8 = 40 28 + -15t = 40 + -16t Solving 28 + -15t = 40 + -16t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '16t' to each side of the equation. 28 + -15t + 16t = 40 + -16t + 16t Combine like terms: -15t + 16t = 1t 28 + 1t = 40 + -16t + 16t Combine like terms: -16t + 16t = 0 28 + 1t = 40 + 0 28 + 1t = 40 Add '-28' to each side of the equation. 28 + -28 + 1t = 40 + -28 Combine like terms: 28 + -28 = 0 0 + 1t = 40 + -28 1t = 40 + -28 Combine like terms: 40 + -28 = 12 1t = 12 Divide each side by '1'. t = 12 Simplifying t = 12
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