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Simplifying 2(t + -3) + -3(2t + -7) = 8 + -6(4t + 1) Reorder the terms: 2(-3 + t) + -3(2t + -7) = 8 + -6(4t + 1) (-3 * 2 + t * 2) + -3(2t + -7) = 8 + -6(4t + 1) (-6 + 2t) + -3(2t + -7) = 8 + -6(4t + 1) Reorder the terms: -6 + 2t + -3(-7 + 2t) = 8 + -6(4t + 1) -6 + 2t + (-7 * -3 + 2t * -3) = 8 + -6(4t + 1) -6 + 2t + (21 + -6t) = 8 + -6(4t + 1) Reorder the terms: -6 + 21 + 2t + -6t = 8 + -6(4t + 1) Combine like terms: -6 + 21 = 15 15 + 2t + -6t = 8 + -6(4t + 1) Combine like terms: 2t + -6t = -4t 15 + -4t = 8 + -6(4t + 1) Reorder the terms: 15 + -4t = 8 + -6(1 + 4t) 15 + -4t = 8 + (1 * -6 + 4t * -6) 15 + -4t = 8 + (-6 + -24t) Combine like terms: 8 + -6 = 2 15 + -4t = 2 + -24t Solving 15 + -4t = 2 + -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. 15 + -4t + 24t = 2 + -24t + 24t Combine like terms: -4t + 24t = 20t 15 + 20t = 2 + -24t + 24t Combine like terms: -24t + 24t = 0 15 + 20t = 2 + 0 15 + 20t = 2 Add '-15' to each side of the equation. 15 + -15 + 20t = 2 + -15 Combine like terms: 15 + -15 = 0 0 + 20t = 2 + -15 20t = 2 + -15 Combine like terms: 2 + -15 = -13 20t = -13 Divide each side by '20'. t = -0.65 Simplifying t = -0.65
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