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Simplifying 3(t + -1) + -4(2t + -1) = 7 + -8(3t + 1) Reorder the terms: 3(-1 + t) + -4(2t + -1) = 7 + -8(3t + 1) (-1 * 3 + t * 3) + -4(2t + -1) = 7 + -8(3t + 1) (-3 + 3t) + -4(2t + -1) = 7 + -8(3t + 1) Reorder the terms: -3 + 3t + -4(-1 + 2t) = 7 + -8(3t + 1) -3 + 3t + (-1 * -4 + 2t * -4) = 7 + -8(3t + 1) -3 + 3t + (4 + -8t) = 7 + -8(3t + 1) Reorder the terms: -3 + 4 + 3t + -8t = 7 + -8(3t + 1) Combine like terms: -3 + 4 = 1 1 + 3t + -8t = 7 + -8(3t + 1) Combine like terms: 3t + -8t = -5t 1 + -5t = 7 + -8(3t + 1) Reorder the terms: 1 + -5t = 7 + -8(1 + 3t) 1 + -5t = 7 + (1 * -8 + 3t * -8) 1 + -5t = 7 + (-8 + -24t) Combine like terms: 7 + -8 = -1 1 + -5t = -1 + -24t Solving 1 + -5t = -1 + -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. 1 + -5t + 24t = -1 + -24t + 24t Combine like terms: -5t + 24t = 19t 1 + 19t = -1 + -24t + 24t Combine like terms: -24t + 24t = 0 1 + 19t = -1 + 0 1 + 19t = -1 Add '-1' to each side of the equation. 1 + -1 + 19t = -1 + -1 Combine like terms: 1 + -1 = 0 0 + 19t = -1 + -1 19t = -1 + -1 Combine like terms: -1 + -1 = -2 19t = -2 Divide each side by '19'. t = -0.1052631579 Simplifying t = -0.1052631579
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