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Simplifying 2(t + -5) + -3(2t + -7) = 12 + -5(3t + 1) Reorder the terms: 2(-5 + t) + -3(2t + -7) = 12 + -5(3t + 1) (-5 * 2 + t * 2) + -3(2t + -7) = 12 + -5(3t + 1) (-10 + 2t) + -3(2t + -7) = 12 + -5(3t + 1) Reorder the terms: -10 + 2t + -3(-7 + 2t) = 12 + -5(3t + 1) -10 + 2t + (-7 * -3 + 2t * -3) = 12 + -5(3t + 1) -10 + 2t + (21 + -6t) = 12 + -5(3t + 1) Reorder the terms: -10 + 21 + 2t + -6t = 12 + -5(3t + 1) Combine like terms: -10 + 21 = 11 11 + 2t + -6t = 12 + -5(3t + 1) Combine like terms: 2t + -6t = -4t 11 + -4t = 12 + -5(3t + 1) Reorder the terms: 11 + -4t = 12 + -5(1 + 3t) 11 + -4t = 12 + (1 * -5 + 3t * -5) 11 + -4t = 12 + (-5 + -15t) Combine like terms: 12 + -5 = 7 11 + -4t = 7 + -15t Solving 11 + -4t = 7 + -15t Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15t' to each side of the equation. 11 + -4t + 15t = 7 + -15t + 15t Combine like terms: -4t + 15t = 11t 11 + 11t = 7 + -15t + 15t Combine like terms: -15t + 15t = 0 11 + 11t = 7 + 0 11 + 11t = 7 Add '-11' to each side of the equation. 11 + -11 + 11t = 7 + -11 Combine like terms: 11 + -11 = 0 0 + 11t = 7 + -11 11t = 7 + -11 Combine like terms: 7 + -11 = -4 11t = -4 Divide each side by '11'. t = -0.3636363636 Simplifying t = -0.3636363636
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