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Simplifying 3(t + -1) + -7(2t + -1) = 2 + -8(3t + 1) Reorder the terms: 3(-1 + t) + -7(2t + -1) = 2 + -8(3t + 1) (-1 * 3 + t * 3) + -7(2t + -1) = 2 + -8(3t + 1) (-3 + 3t) + -7(2t + -1) = 2 + -8(3t + 1) Reorder the terms: -3 + 3t + -7(-1 + 2t) = 2 + -8(3t + 1) -3 + 3t + (-1 * -7 + 2t * -7) = 2 + -8(3t + 1) -3 + 3t + (7 + -14t) = 2 + -8(3t + 1) Reorder the terms: -3 + 7 + 3t + -14t = 2 + -8(3t + 1) Combine like terms: -3 + 7 = 4 4 + 3t + -14t = 2 + -8(3t + 1) Combine like terms: 3t + -14t = -11t 4 + -11t = 2 + -8(3t + 1) Reorder the terms: 4 + -11t = 2 + -8(1 + 3t) 4 + -11t = 2 + (1 * -8 + 3t * -8) 4 + -11t = 2 + (-8 + -24t) Combine like terms: 2 + -8 = -6 4 + -11t = -6 + -24t Solving 4 + -11t = -6 + -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. 4 + -11t + 24t = -6 + -24t + 24t Combine like terms: -11t + 24t = 13t 4 + 13t = -6 + -24t + 24t Combine like terms: -24t + 24t = 0 4 + 13t = -6 + 0 4 + 13t = -6 Add '-4' to each side of the equation. 4 + -4 + 13t = -6 + -4 Combine like terms: 4 + -4 = 0 0 + 13t = -6 + -4 13t = -6 + -4 Combine like terms: -6 + -4 = -10 13t = -10 Divide each side by '13'. t = -0.7692307692 Simplifying t = -0.7692307692
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