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Simplifying 2(t + -1) + -3(5t + -1) = 12 + -5(6t + 5) Reorder the terms: 2(-1 + t) + -3(5t + -1) = 12 + -5(6t + 5) (-1 * 2 + t * 2) + -3(5t + -1) = 12 + -5(6t + 5) (-2 + 2t) + -3(5t + -1) = 12 + -5(6t + 5) Reorder the terms: -2 + 2t + -3(-1 + 5t) = 12 + -5(6t + 5) -2 + 2t + (-1 * -3 + 5t * -3) = 12 + -5(6t + 5) -2 + 2t + (3 + -15t) = 12 + -5(6t + 5) Reorder the terms: -2 + 3 + 2t + -15t = 12 + -5(6t + 5) Combine like terms: -2 + 3 = 1 1 + 2t + -15t = 12 + -5(6t + 5) Combine like terms: 2t + -15t = -13t 1 + -13t = 12 + -5(6t + 5) Reorder the terms: 1 + -13t = 12 + -5(5 + 6t) 1 + -13t = 12 + (5 * -5 + 6t * -5) 1 + -13t = 12 + (-25 + -30t) Combine like terms: 12 + -25 = -13 1 + -13t = -13 + -30t Solving 1 + -13t = -13 + -30t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '30t' to each side of the equation. 1 + -13t + 30t = -13 + -30t + 30t Combine like terms: -13t + 30t = 17t 1 + 17t = -13 + -30t + 30t Combine like terms: -30t + 30t = 0 1 + 17t = -13 + 0 1 + 17t = -13 Add '-1' to each side of the equation. 1 + -1 + 17t = -13 + -1 Combine like terms: 1 + -1 = 0 0 + 17t = -13 + -1 17t = -13 + -1 Combine like terms: -13 + -1 = -14 17t = -14 Divide each side by '17'. t = -0.8235294118 Simplifying t = -0.8235294118
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