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Simplifying -8(t + -4) + 7 = 4[t + -3(1 + -1t)] + 6 Reorder the terms: -8(-4 + t) + 7 = 4[t + -3(1 + -1t)] + 6 (-4 * -8 + t * -8) + 7 = 4[t + -3(1 + -1t)] + 6 (32 + -8t) + 7 = 4[t + -3(1 + -1t)] + 6 Reorder the terms: 32 + 7 + -8t = 4[t + -3(1 + -1t)] + 6 Combine like terms: 32 + 7 = 39 39 + -8t = 4[t + -3(1 + -1t)] + 6 39 + -8t = 4[t + (1 * -3 + -1t * -3)] + 6 39 + -8t = 4[t + (-3 + 3t)] + 6 Reorder the terms: 39 + -8t = 4[-3 + t + 3t] + 6 Combine like terms: t + 3t = 4t 39 + -8t = 4[-3 + 4t] + 6 39 + -8t = [-3 * 4 + 4t * 4] + 6 39 + -8t = [-12 + 16t] + 6 Reorder the terms: 39 + -8t = -12 + 6 + 16t Combine like terms: -12 + 6 = -6 39 + -8t = -6 + 16t Solving 39 + -8t = -6 + 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. 39 + -8t + -16t = -6 + 16t + -16t Combine like terms: -8t + -16t = -24t 39 + -24t = -6 + 16t + -16t Combine like terms: 16t + -16t = 0 39 + -24t = -6 + 0 39 + -24t = -6 Add '-39' to each side of the equation. 39 + -39 + -24t = -6 + -39 Combine like terms: 39 + -39 = 0 0 + -24t = -6 + -39 -24t = -6 + -39 Combine like terms: -6 + -39 = -45 -24t = -45 Divide each side by '-24'. t = 1.875 Simplifying t = 1.875
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