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Simplifying 8(t + 2) + 5(5t + 2) = 32(t + 1) + 6 Reorder the terms: 8(2 + t) + 5(5t + 2) = 32(t + 1) + 6 (2 * 8 + t * 8) + 5(5t + 2) = 32(t + 1) + 6 (16 + 8t) + 5(5t + 2) = 32(t + 1) + 6 Reorder the terms: 16 + 8t + 5(2 + 5t) = 32(t + 1) + 6 16 + 8t + (2 * 5 + 5t * 5) = 32(t + 1) + 6 16 + 8t + (10 + 25t) = 32(t + 1) + 6 Reorder the terms: 16 + 10 + 8t + 25t = 32(t + 1) + 6 Combine like terms: 16 + 10 = 26 26 + 8t + 25t = 32(t + 1) + 6 Combine like terms: 8t + 25t = 33t 26 + 33t = 32(t + 1) + 6 Reorder the terms: 26 + 33t = 32(1 + t) + 6 26 + 33t = (1 * 32 + t * 32) + 6 26 + 33t = (32 + 32t) + 6 Reorder the terms: 26 + 33t = 32 + 6 + 32t Combine like terms: 32 + 6 = 38 26 + 33t = 38 + 32t Solving 26 + 33t = 38 + 32t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-32t' to each side of the equation. 26 + 33t + -32t = 38 + 32t + -32t Combine like terms: 33t + -32t = 1t 26 + 1t = 38 + 32t + -32t Combine like terms: 32t + -32t = 0 26 + 1t = 38 + 0 26 + 1t = 38 Add '-26' to each side of the equation. 26 + -26 + 1t = 38 + -26 Combine like terms: 26 + -26 = 0 0 + 1t = 38 + -26 1t = 38 + -26 Combine like terms: 38 + -26 = 12 1t = 12 Divide each side by '1'. t = 12 Simplifying t = 12
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