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Simplifying 2(t + -5) + -3(5t + -6) = 7 + -5(6t + 1) Reorder the terms: 2(-5 + t) + -3(5t + -6) = 7 + -5(6t + 1) (-5 * 2 + t * 2) + -3(5t + -6) = 7 + -5(6t + 1) (-10 + 2t) + -3(5t + -6) = 7 + -5(6t + 1) Reorder the terms: -10 + 2t + -3(-6 + 5t) = 7 + -5(6t + 1) -10 + 2t + (-6 * -3 + 5t * -3) = 7 + -5(6t + 1) -10 + 2t + (18 + -15t) = 7 + -5(6t + 1) Reorder the terms: -10 + 18 + 2t + -15t = 7 + -5(6t + 1) Combine like terms: -10 + 18 = 8 8 + 2t + -15t = 7 + -5(6t + 1) Combine like terms: 2t + -15t = -13t 8 + -13t = 7 + -5(6t + 1) Reorder the terms: 8 + -13t = 7 + -5(1 + 6t) 8 + -13t = 7 + (1 * -5 + 6t * -5) 8 + -13t = 7 + (-5 + -30t) Combine like terms: 7 + -5 = 2 8 + -13t = 2 + -30t Solving 8 + -13t = 2 + -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. 8 + -13t + 30t = 2 + -30t + 30t Combine like terms: -13t + 30t = 17t 8 + 17t = 2 + -30t + 30t Combine like terms: -30t + 30t = 0 8 + 17t = 2 + 0 8 + 17t = 2 Add '-8' to each side of the equation. 8 + -8 + 17t = 2 + -8 Combine like terms: 8 + -8 = 0 0 + 17t = 2 + -8 17t = 2 + -8 Combine like terms: 2 + -8 = -6 17t = -6 Divide each side by '17'. t = -0.3529411765 Simplifying t = -0.3529411765
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